AP Physics 2: Algebra-Based FRQ Room
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AP Physics 2: Algebra-Based Free Response Questions
The best way to get better at FRQs is practice. Browse through dozens of practice AP Physics 2: Algebra-Based FRQs to get ready for the big day.
Airflow Over a Wing
An airplane wing has a surface area of 16 m². The pressure difference between the bottom and the top
Analyzing a High-Speed Water Jet
A garden hose with an initial inner diameter of $$2\;cm$$ is fitted with a nozzle that reduces the d
Analyzing Submerged Structures in Fluids
A marine structure is designed to float partially submerged in a lake. The structure has a total mas
Bernoulli's Equation Application
A horizontal pipe has a constriction such that the cross-sectional area at Section 2 is one-third of
Bernoulli’s Equation in a Constricted Pipe
A fluid flows through a horizontal pipe that gradually constricts. At the wide section (Point 1) the
Bernoulli’s Equation in a Constricted Pipe
A pump forces water through a horizontal pipe that gradually constricts. At point 1 (where the pipe
Bernoulli's Equation in a Horizontal Pipe
A horizontal pipe carries water and gradually narrows. In the wide Section 1 (diameter 8 cm), the wa
Bernoulli's Equation in Pipe Flow
A pump forces water through a horizontal pipe that includes a constriction. At Point 1 (just after t
Bernoulli's Principle and Aircraft Lift
Air flows over the upper and lower surfaces of an airplane wing. In a certain section along the wing
Buoyancy and Archimedes’ Principle Experiment
An object with a mass of $$150\,kg$$ and a volume of $$0.75\,m^3$$ floats in a fluid of unknown dens
Buoyancy and Archimedes' Principle Investigation
In a laboratory experiment, a researcher investigates the buoyancy of objects using ethyl alcohol (d
Buoyancy and Floating Objects
An object with a mass of 150 kg and a volume of 0.75 m³ is placed in a fluid with a density of 800 k
Buoyancy and Stability of a Floating Body
A rectangular boat with a flat bottom is floating in freshwater (density = 1000 kg/m³). The boat has
Buoyancy in a Variable-Density Atmosphere: Weather Balloon Analysis
A weather balloon is launched at ground level, where the atmospheric density is $$1.225\,kg/m^3$$. A
Capillary Action: Investigating the Rise of Liquid in Narrow Tubes
Design an experiment to measure the capillary rise of a liquid in tubes of various diameters. Your e
Comparative Study of Fluids Using a U-Tube Manometer
In a laboratory, students use a U-tube manometer to compare the densities of two unknown fluids. The
Comparing Fluid Pressures in Different Media
Two open-top tanks contain different fluids. Tank 1 is filled with water (density = $$1000 \cdot kg/
Composite Material Density and Pressure Analysis
A materials scientist tests a new composite material by first measuring a 0.001 m³ sample with a mas
Compressibility Effects in High-Pressure Fluid Systems
In a high-pressure hydraulic system, fluid compressibility effects, though typically small in liquid
Continuity Equation and Flow Rate
Water flows through a circular pipe. At Section 1, the pipe has a radius of $$2\,cm$$ and the water
Continuity Equation in a Variable Diameter Pipe
A circular pipe carries water with an initial section having a radius of 2 cm and a flow speed of 6
Continuity Equation in Branching Pipes
A pipeline carrying water (density $$1000\;kg/m^3$$) splits into two branches. The main pipe has a f
Density Determination from Experimental Data
In an experiment to measure the density of various liquids, a student recorded the following data:
Designing a Pipeline: Balancing Pressure and Flow Rate
An engineering project requires designing a pipeline to transport water over long distances. Changes
Designing a Water Fountain: Pressure and Flow
A landscape architect is designing a water fountain and needs the water jet to reach a maximum heigh
Determining Fluid Density
A sample of an unknown liquid has a mass of $$1.2 \times 10^{0} \text{ kg}$$ and occupies a volume o
Experimental Analysis of Lift Generation
In wind tunnel experiments, an airfoil is tested under varying flow speeds. A table gives measured d
Experimental Determination of Fluid Density
This problem requires designing an experiment using the buoyant force method to determine the densit
Flow Rate and Energy Losses in Pipe Constriction
A horizontal pipe has an initial radius of 3.0 cm and narrows to a radius of 1.5 cm. Water flows wit
Flow Rate Conundrum in a Diverging-Nozzle Experiment
A diverging-converging nozzle experiment reports that increasing the nozzle diameter leads to a decr
Flow Rate Experiment with Variable Pipe Diameters
A mechanical engineer conducts an experiment in a pipe where the diameter changes in three sequentia
Fluid Pressure on a Dam Wall
A civil engineer is evaluating the force exerted on a vertical dam wall by the water in a reservoir.
Graphical Analysis of Flow Continuity
This problem uses a provided graph to analyze the relationship between flow speed and pipe cross-sec
Graphical Analysis of Hydrostatic Pressure in a Water Tower
A water tower supplies water to a town, and the gauge pressure measured in the town varies with the
Hydrostatic Pressure in a Fluid
Consider an open tank containing water. The water has a density of 1000 kg/m³. Atmospheric pressure
Hydrostatic Pressure Miscalculation Experiment
A student sets up an experiment to measure the pressure at the bottom of a water tank. The student f
Investigating Fluid Oscillations in a U-Tube
A U-tube containing a fluid is displaced from equilibrium and allowed to oscillate. Analyze the osci
Investigating Fluid Pressure with a Manometer
A researcher employs a U-tube manometer to measure the gauge pressure in a pressurized system using
Investigating Pressure Differences in Fluid Circuits
A U-shaped tube contains a fluid with a density of 1200 kg/m³. A small height difference between the
Lift Force Measurement in Wind Tunnel
In a wind tunnel experiment, a wing model is tested under controlled airflow. Pressure sensors at tw
Mapping Fluid Pressure Distribution Using Sensors
Design an experiment to map the pressure distribution within a fluid container by using multiple pre
Measuring Buoyant Force with a Submerged Object
A student conducts an experiment to measure the buoyant force acting on an object of volume $$0.2 \c
Measuring Hydrostatic Pressure in an Underwater Environment
An oceanographer sets up an experiment to measure the hydrostatic pressure as a function of depth in
Mercury Barometer Atmospheric Pressure Measurement
An experiment employs a mercury barometer to measure atmospheric pressure. The claim is that the hei
Multi-Stage Fluid Dynamics Analysis in a Piping Network
A fluid flows through a piping network with three segments having different diameters and elevation
Non-uniform Flow Channel Velocity Measurement Error
A student designs an experiment to measure the velocity of water in an open channel that has section
Non-uniform Flow Through Constricted Channel Error
A student constructs an apparatus to measure fluid velocity in a channel that narrows and changes sh
Open Channel Pressure Measurement
In an open channel flow experiment, gauge pressures were measured at different depths below the free
Optimization of Fluid Flow in Industrial Piping Systems
An industrial piping system includes a segment where the pipe narrows from a diameter of 0.3 m to a
Pipeline Flow Optimization in a Water Treatment Facility
A water treatment facility operates a pipeline that has three sections with varying diameters. The f
Pressure at an Interface of Two Fluids
A container holds two immiscible fluids. A layer of oil (density $$800\;kg/m^3$$, depth $$0.5\;m$$)
Pressure Calculations in Submerged Structures
A structural engineering team is testing a scale model of a submerged tunnel to study the effects of
Pressure Distribution on a Submerged Plate
A researcher is studying the pressure distribution on a vertical rectangular plate submerged in wate
Pump Power in a Multi-Elevation Piping System
A pump moves water (density = 1000 kg/m³) through a piping system where the water is elevated by 2 m
Pump Work Analysis in a Closed Fluid Circuit
In a closed fluid circuit, a pump is used to circulate water so that it maintains a constant flow ra
Siphon Action Analysis
A siphon is used to transfer water from a container. The highest point of the siphon tube is 2 m abo
Tank Discharge Flow Experiment
An experiment investigates the discharge of water from a tank through a small orifice at the bottom.
Time-Varying Fluid Flow Analysis
In an experiment, the volume flow rate of water through a horizontal pipe is found to vary with time
Venturi Meter Flow Measurement
A Venturi meter is used to measure the flow rate in a pipe by recording the pressure difference betw
Viscosity Effects on Flow Rate in Capillary Tubes
Design an experiment to study how fluid viscosity affects the flow rate through capillary tubes. You
Visualization of Laminar Flow in Pipes
In an experiment designed to visualize the velocity profile of a fluid in a pipe, sensors are placed
Wind Tunnel Dynamic Pressure Measurement Error
A student performs an experiment in a wind tunnel to measure dynamic pressure using a pitot tube. Th
Analysis of a Carnot Cycle
A Carnot engine operates between two thermal reservoirs with temperatures $$T_H$$ and $$T_C$$. A cyc
Analysis of Atmospheric Pressure and Gas Density
Explain why the high pressure generated by confined gas does not cause the container lid to pop off,
Analysis of Conduction, Convection, and Radiation in Heat Transfer Experiment
An experiment is designed to study different modes of heat transfer. In one part of the experiment,
Analyzing Deviations from the Ideal Gas Law
A researcher measures the pressure of a gas at various volumes and observes deviations from the Idea
Average Kinetic Energy and RMS Velocity in Gases
Using the kinetic theory of gases, consider a sample of an ideal gas at T = 300 K. (a) Calculate the
Calculating Work and Efficiency in a Heat Engine Cycle
A heat engine undergoes a cycle in which it absorbs $$Q_H = 1000 J$$ of heat and rejects $$Q_C = 400
Comparative Study of Heat Transfer Modes in Earth's Atmosphere
Understanding heat transfer in the Earth’s atmosphere is crucial for climate modeling. The three pri
Comparing Isothermal and Adiabatic Processes in a P-V Diagram Experiment
An experiment uses a P-V diagram to compare isothermal and adiabatic processes. Two distinct paths a
Conduction Heat Transfer Analysis
A metal rod is used to conduct heat between two reservoirs. The rod has a thermal conductivity of $$
Conduction, Specific Heat, and Temperature Change
A metal rod of mass 2 kg and specific heat capacity 400 J/(kg·K) is heated by supplying 8000 J of en
Designing a Controlled Experiment for Ideal Gas Behavior
A scientist is planning an experiment to test the Ideal Gas Law $$PV = nRT$$ under controlled condit
Designing a Thermos: Minimizing Heat Transfer
A thermos is designed to keep liquids hot by minimizing heat transfer. Discuss the design features c
Efficiency of a Refrigeration Cycle
A refrigerator operates between a cold reservoir at $$280\;K$$ and a warm reservoir at $$300\;K$$.
Entropy Change in a Thermodynamic Cycle
During a cyclic process, an experiment measures the change in entropy during various stages. Analyze
Entropy Change in Gas Mixing Experiment
Two chambers, each containing 0.5 moles of an identical ideal gas at 300 K and with a volume of 0.01
Entropy Changes in Thermodynamic Processes
Consider an ideal gas that undergoes an isothermal expansion from an initial volume $$V_1$$ to a fin
Evaluating the Role of Pressure Differences in Atmospheric Applications
A high-altitude weather balloon collects data on atmospheric pressure as it ascends. The recorded da
First Law in a Cyclic Process
A closed system undergoes a cyclic process involving isothermal, isobaric, and adiabatic steps. Answ
Heat Engine Efficiency
A heat engine draws $$800\;J$$ of heat from a high-temperature source and rejects $$450\;J$$ of heat
Heat Engine Efficiency and Energy Analysis
A heat engine operates in cycles, drawing heat from a high-temperature reservoir and rejecting part
Heat Engines: Efficiency and Work Calculations
A heat engine operates in a cycle, drawing 800 J of heat from a high-temperature source and rejectin
Ideal Gas: Container Pressure and Force
Consider a cylindrical container of gas with a radius $$r = 0.15\;m$$ and height $$h = 0.30\;m$$ tha
Investigating Temperature and Pressure Effects on Gas Behavior
In a laboratory experiment, gas pressures were measured at various temperatures while keeping the vo
Investigating the Role of Atmospheric Pressure in Sealed Container Systems
The net force on a container’s lid results from the difference between the internal gas pressure and
Kinetic Energy and Molecular Speeds
The average kinetic energy of gas molecules is given by $$K_{avg} = \frac{3}{2} k_B T$$. (a) Derive
Molecular Speed and Temperature
Consider an ideal gas composed of molecules each having mass m. The root‐mean‐square speed is given
Net Work in a Cyclic Thermodynamic Process
A cyclic thermodynamic process is depicted in a provided P–V diagram. Summarize the key characterist
Thermodynamic Analysis of an Ice Melting Process
When heat is added to a substance at its melting point, the phase change occurs without a change in
Time-Resolved Thermal Imaging Experiment Error
A student uses a thermal imaging camera to study the cooling rates of a heated brick as it returns t
Transient Heat Conduction Analysis
The transient heat conduction in a solid can be described by the heat equation: $$\frac{\partial T}{
Work Done in a Non-Constant Pressure Process
An ideal gas is compressed in a cylinder by a piston, and the pressure inside the cylinder varies wi
Analysis of an Electric Dipole Field
An electric dipole consists of two charges, \(+q\) and \(-q\), separated by a distance \(d\). (a) D
Analyzing Electric Field Variation Above a Charged Plate
An experiment measured the electric potential at various distances from a large, uniformly charged p
Balancing Forces in a Uniform Electric Field
An object of mass $$5.0 \; g$$ (0.005 kg) is placed 2.0 cm above a large, positively charged horizon
Balancing Gravitational and Electric Forces in a Uniform Field
A small object of mass 5.0 g is placed 2.0 cm above a large, positively charged horizontal plate tha
Charge Distribution on Conductors vs. Insulators
Two identical spheres are made, one of conductive metal and the other of insulating glass, and both
Charge Induction in Connected Conducting Spheres
In an induction experiment, two neutral conducting spheres are brought into contact while a charged
Charge Redistribution Experiment
An experiment is designed to verify the conservation of charge during collisions between conducting
Charging Methods and Redistribution of Charge
Two identical, initially neutral conducting spheres are brought into contact. Then, a positively cha
Comparative Analysis of Charging Methods
In a laboratory setting, two objects made from different materials—one metal (a good conductor) and
Comparing Electric and Gravitational Forces in a Hydrogen Atom
Consider theoretical estimates for the forces acting between a proton and an electron in a hydrogen
Comparison of Dipole and Monopole Field Mapping
A simulation experiment compares equipotential maps for a single point charge (monopole) and for a d
Design of a Charging by Induction Experiment
Two initially neutral conducting spheres are to be charged by induction. Design an experiment to dem
Dipole Electric Field at Midpoint
A dipole is formed by two point charges of +4.0 nC and -4.0 nC separated by a distance of 6.0 cm. De
Dipole Electric Field Calculation and Explanation
A dipole is formed by two point charges: a positive charge of $$+4.0*10^{-9}$$ C and a negative char
Distance Dependence in Coulomb's Law
Coulomb's Law quantitatively describes the force between two point charges as inversely proportional
Effect of a Non-uniform Electric Field on a Moving Charge
A charged particle with charge $$q$$ is accelerated through a non-uniform electric field generated b
Effect of Plate Separation on Capacitance in a Parallel-Plate Capacitor
A parallel-plate capacitor is constructed with plates of area A = 0.02 m². The separation between th
Electric Dipole Analysis
A researcher studies an electric dipole consisting of a positive charge of $$+4.0 \; nC$$ and a nega
Electric Field from an Infinite Charged Sheet
Consider a large sheet with a uniform surface charge density σ = 1.5 × 10⁻⁶ C/m².
Electric Field from Multiple Point Charges
This question involves computing the net electric field at a specific point due to three point charg
Electric Field Lines at Media Boundaries
This problem examines how electric field lines behave at the boundary between two different media an
Electric Potential Dependence Experiment
An experiment is conducted to measure the electric potential at various distances from a fixed point
Electric Potential from Multiple Point Charges
Two fixed point charges, $$Q_1$$ and $$Q_2$$, are located at specified positions. A point A is locat
Electric Potential Variation in a Conical Capacitor
A non-standard capacitor is constructed with one plate conically shaped, leading to non-uniform sepa
Equilibrium of an Object in a Uniform Electric Field
An object of mass 5 g is suspended in a uniform electric field of $$1.0*10^{6}$$ N/C such that the u
Equipotential Surfaces and Field Lines
A researcher maps the equipotential surfaces around an isolated charged sphere.
Experimental Analysis of Charge Quantization
Design an experiment that demonstrates the quantization of electric charge using either the oil drop
Force and Potential Energy in the Hydrogen Atom
For a hydrogen atom, consider the proton and electron separated by a distance of 0.5×10^-10 m. Using
Forces in the Hydrogen Atom
Consider a hydrogen atom in which a proton (mass = 1.6×10⁻²⁷ kg, charge +e) and an electron (mass =
Fringing Fields in Parallel-Plate Capacitors
In a real parallel-plate capacitor, the electric field near the edges deviates from the ideal unifor
Graphical Analysis of Electric Field Variation with Distance
Experimental measurements were made of the electric field strength at varying distances from a charg
Investigating Coulomb's Law in a Controlled Experiment
Design an experiment to measure the electric force between two charged spheres as a function of sepa
Kinetic Energy Gain from Electric Potential Energy Loss
A negative charge of magnitude q = -1×10⁻⁸ C is released from rest at a distance of 10 cm from a fix
Kinetic Energy Gain from Electrical Potential Energy Change
A fixed charge \(q_1 = +2 \times 10^{-6} \; C\) and a mobile charge \(q_2 = -1 \times 10^{-8} \; C\)
Kinetic Energy Gain of a Test Charge in a Non-Uniform Electric Field
A test charge of $$q = +5.0 \times 10^{-9}\,C$$ is released from rest at a distance of $$0.20\,m$$ f
Mapping Electric Field Around a Point Charge
Design an experiment to map the electric field in the vicinity of a point charge using a test charge
Millikan Oil Drop Experiment Analysis
The Millikan oil drop experiment played a pivotal role in determining the fundamental charge of the
Non-Uniform Charge Distribution Effects
A researcher examines the electric field created by a hemispherical charge distribution with total c
Parallel Plate Capacitor Experiment: Dielectric Misconception
An experiment is designed to measure the capacitance of a parallel-plate capacitor by arranging two
Potential Difference in a Parallel-Plate Capacitor
A parallel-plate capacitor has plates of area A = 0.05 m² separated by a distance d = 0.001 m and is
Potential Energy Change in a Uniform Field
In a controlled experiment, a charged particle initially at rest moves through a uniform electric fi
Proton-Electron Force Comparison
This question examines the forces between a proton and an electron in a hydrogen atom and requires y
Series and Parallel Capacitor Network Analysis
A capacitor network is constructed by connecting capacitors in both series and parallel arrangements
Superposition of Electric Fields Experiment
Four identical positively charged spheres are fixed at the vertices of a square, and a negatively ch
Superposition of Electric Fields: Square Charge Configuration
Four identical positive point charges are fixed at the vertices of a square with side length 0.20 m.
Surface Charge Distribution on Irregular Conductors
The distribution of surface charge on conductors is influenced by the geometry of the surface. This
Verification of the Inverse Square Law for Electric Forces
An experiment measured the electric force between two charged objects as the distance between them w
Work and Electrical Potential Energy in a Uniform Electric Field
A positive charge q = 1.0 × 10⁻⁶ C is moved a distance d = 0.05 m in the direction of a uniform elec
Work and Potential Difference in a Uniform Electric Field
A positive charge of $$+1.0*10^{-2}$$ C is moved a distance of 0.15 m in the direction of a uniform
Work Calculation in a Non-Uniform Electric Field
An experiment tracks the work done on a charge as it moves through a non-uniform electric field crea
Work Done in a Non-uniform Electric Field
A charged particle experiences a non-uniform electric field given by $$E(y) = 200 \; y \quad (N/C)$$
Work in a Non-Uniform Electric Field
A researcher moves a charge in the non-uniform electric field generated by a fixed point charge. The
Work in a Radial Non-Uniform Electric Field
A positive test charge q is moved radially inward from a distance r₁ to a closer distance r₂ from a
Work Required to Assemble a Triangular System of Point Charges
Three point charges are fixed in place forming a triangle. The charges and separations are: Q₁ = +2.
Analyzing Series-Parallel Combinations of Capacitors
Capacitors can be combined in series or parallel to yield different equivalent capacitances. Answer
Analyzing the Effect of Wire Geometry on Resistance Measurements
A student investigates how the resistance of a wire depends on its length and cross-sectional area b
Analyzing Transients in RC Circuits with Switching
Consider a circuit where a capacitor, initially uncharged, is connected in series with a resistor an
Capacitor Combinations and Equivalent Capacitance
A circuit contains three capacitors with the following capacitances: 4 μF, 6 μF, and 12 μF. In the c
Capacitors in Series and Parallel: Equivalent Capacitance Analysis
An experiment is performed using two identical capacitors each with capacitance $$C = 5\;F$$. They a
Designing a Circuit for Energy Efficiency Testing
A recent study claims that by reconfiguring a circuit, the overall power loss in resistors can be mi
Determining Capacitance Changes Due to Physical Adjustments
A parallel-plate capacitor has plate area A, plate separation d, and a dielectric constant k. Answer
Discharging of a Capacitor in an RC Circuit
A capacitor initially charged to $$12 \text{ V}$$ is discharged through a resistor of $$4 \Omega$$.
Effect of Adding a Parallel Resistor in a Series Circuit
Consider a circuit consisting of a 9 V battery connected in series with a 12 Ω resistor. A 24 Ω resi
Effect of Dielectric on Capacitance in a Parallel-Plate Capacitor
A parallel-plate capacitor with plate area A and separation d is initially filled with air (dielectr
Effect of Wire Dimensions on Resistance
The resistance of a wire is given by $$R = \rho*\frac{l}{A}$$, where $$l$$ is the length, $$A$$ is t
Effects of Altering Capacitance in a Charged Capacitor Circuit
A capacitor is first charged in a circuit with a battery connected, and then the battery is disconne
Effects of Altering Capacitance on a Charged Capacitor
A capacitor with an initial capacitance of $$10\,\mu F$$ is charged to $$12\,V$$ by a battery, and t
Equivalent Resistance in Complex Resistor Networks
A circuit consists of five resistors arranged as follows: Resistors $$R_1$$ and $$R_2$$ (each $$10\,
Evaluating a Modified Ammeter Design for Improved Accuracy in Low-Current Measurements
A claim has been made that a newly designed ammeter with ultra-low internal resistance provides sign
Experimental Circuit Measurements Analysis
A researcher records experimental data from a circuit using a voltmeter and an ammeter. The data is
Graphical Analysis of Battery Discharge
A battery is discharged over time and its terminal voltage is recorded. The following graph shows th
Heat Generation and Power Dissipation in Resistors
A circuit experiment provides measurements of voltage and current for different resistors. Use the d
Impact of Internal Resistance on Battery Performance
A battery with an electromotive force (EMF) of $$9\,V$$ and an internal resistance of $$1\,\Omega$$
Investigating Battery Internal Resistance using a Series Circuit
A student designs an experiment to measure the internal resistance (r) of a battery. The setup consi
Investigating Short-Circuit Effects in a Capacitor-Resistor Circuit
Short-circuiting a charged capacitor can lead to extremely high transient currents. Answer the follo
Modifying Resistor Values for Current Limiting in LED Circuits
An LED with a voltage drop of 2 V requires a current of 20 mA for optimal performance. It is powered
Multi-branch Circuit Analysis
A complex circuit consists of two branches: Branch A contains two resistors (4 Ω and 3 Ω) in series,
Power Dissipation Analysis
A resistor with resistance $$R = 50\,\Omega$$ is connected across a 20 V battery. Calculate:
Power Dissipation in Circuit Components
A simple circuit consists of a resistor connected to a battery. Consider a scenario where a 9 V batt
RC Circuit Transients and Time Constants
An RC circuit is comprised of a resistor $$R = 5\times10^3\,\Omega$$ and a capacitor $$C = 2\,\mu F$
Resistor Network Analysis
Consider a circuit where a 4 Ω resistor is connected in series with a parallel combination of a 3 Ω
Series and Parallel Circuit Analysis
In this problem, you will analyze a circuit that comprises a combination of resistors in both series
Series Circuit Analysis and Ohm's Law Application
A battery of 9 V is connected in series with two resistors: one having a resistance of 100 Ω and the
Studying the Transient Response in an RC Circuit with a Variable Resistor
A student investigates the charging process of a capacitor in an RC circuit by connecting a 12 V bat
Transient and Steady State Analysis in RC Circuit
Consider an RC circuit with a resistor $$R = 1\times10^3\,\Omega$$, a capacitor $$C = 10\,\mu F$$, a
Transient Response in an RC Circuit with Multiple Resistors
Design and analyze a more complex RC circuit that includes multiple resistors in series and parallel
AC Generator Induced EMF Analysis
Consider an alternating current generator where a coil of $$N$$ turns and area $$A$$ rotates in a un
Balancing Forces on a Current-Carrying U-Shaped Wire
In a laboratory experiment, a U-shaped wire is immersed in a region with a uniform magnetic field th
Calculating the Magnetic Field Around a Current-Carrying Wire
A long, straight wire carrying a steady current produces a magnetic field in the space around it. Us
Comparing Magnetic Field Mapping Techniques
Design an experiment to compare two techniques for mapping magnetic field lines: one using iron fili
Designing an Experiment for Faraday's Law
Faraday’s law states that a changing magnetic flux through a circuit induces an emf. Design an exper
Electromagnetic Induction in a Rotating Loop
A single circular loop with a radius of $$r = 0.1 \; m$$ is placed in a uniform magnetic field of st
Electromagnetic Induction in Generators
This FRQ integrates the principles of Faraday's law to model the operation of an electromagnetic gen
Evaluating Solenoid Field Uniformity
In an experiment, the magnetic field inside a solenoid is measured at different positions along its
Exploring Eddy Currents and Energy Dissipation
Eddy currents are induced in conductors when exposed to changing magnetic fields, and they can lead
Force on a Current-Carrying Wire in a Magnetic Field
A straight wire carrying an electric current is placed in a uniform magnetic field. Answer the follo
Force on a Moving Charge
This FRQ focuses on calculating the magnetic force on a moving charge and interpreting its direction
Force on a Moving Charge in a Magnetic Field
A charged particle moves through a uniform magnetic field. Determine the magnetic force acting under
Force on a Moving Charge in a Magnetic Field
A charged particle moves in a uniform magnetic field. Consider a scenario where the particle moves w
Force on a Moving Charge in a Magnetic Field
A charged particle moves through a uniform magnetic field. Analyze the factors affecting the magnitu
Graphical Analysis of Magnetic Flux Change
This FRQ involves analyzing experimental data on magnetic flux change over time, determining the ind
Induced EMF in a Time-Varying Solenoid Field
A solenoid with 300 turns and a cross-sectional area of 0.05 m² produces an axial magnetic field tha
Investigating Motional EMF in a Moving Conductor
In an experiment, a conducting rod of length $$\ell = 0.5\;m$$ is moved at a constant velocity throu
Magnetic Braking in a Rotating Metal Disk
A metal disk is set into rotation and brought near a set of fixed magnets arranged so that eddy curr
Magnetic Dipoles: Bar Magnet and Current Loop
A researcher compares the magnetic field produced by a permanent bar magnet with that produced by a
Magnetic Field Mapping with Iron Filings
Permanent magnets produce complex magnetic fields that can be visualized using iron filings. In this
Magnetic Field Mapping with Iron Filings
A permanent magnet’s surrounding region is investigated using iron filings. Explain how iron filings
Magnetic Field of a Current-Carrying Wire and Force on a Proton
A long, straight wire carries a current of $$I = 10 \; A$$. A proton moving parallel to the wire wit
Magnetic Force vs. Current in a Wire
An experiment examines the magnetic force acting on a straight current-carrying wire placed in a uni
Magnetic Torque on a Current Loop
A rectangular loop of wire with length $$L = 0.1 \; m$$ and width $$w = 0.05 \; m$$ carries a curren
Mapping Magnetic Field Lines
A researcher is investigating the spatial distribution and behavior of magnetic fields around a perm
Mapping Magnetic Field Lines with Iron Dust
A recent experimental report claims that by sprinkling iron dust on a piece of paper placed over a b
Mapping Magnetic Field Using Iron Filings
Students perform an experiment to visualize the magnetic field around a bar magnet by sprinkling iro
Measuring Magnetic Permeability via Compass Deflection
An experiment attempts to determine the magnetic permeability of a material by measuring the deflect
Motional EMF in a Moving Conductor
A conducting rod of length 0.5 m moves at a constant velocity of 3 m/s perpendicular to a uniform ma
Motional EMF in a Moving Rod
A conducting rod of length $$L = 0.3 m$$ moves with a constant velocity of $$v = 2 m/s$$ along paral
Rotating Coil and Faraday’s Law Experiment
Design an experiment to test Faraday’s Law of electromagnetic induction by using a coil rotating in
Solenoid Magnetic Field Measurement Experiment
A team of students sets out to measure the magnetic field inside a solenoid using a Hall effect sens
Time-Dependent Induced EMF in a Rotating Loop
Design an experiment to investigate how the induced emf in a rotating loop varies over time, particu
Uniform Magnetic Field in a Solenoid Experiment
An experiment is conducted using a solenoid as an electromagnet, and it is claimed that the magnetic
Uniform Magnetic Field Inside a Solenoid
A solenoid is constructed with 400 turns and has a length of 0.25 m. It carries a current of 2 A. An
Advanced Thin Lens Systems in Compound Microscopes
A compound microscope uses two converging lenses: an objective lens with a focal length of $$f_o = 0
Converging Lens and Image Formation
Converging lenses project real images through refraction. Analyze an optical scenario involving a co
Convex Mirror Image Analysis
A researcher is examining a convex mirror. An object of height 5 cm is placed 40 cm in front of a co
Convex Mirror Image Formation
An object of height $$h_o = 5 \ cm$$ is placed at a distance of $$d_o = 25 \ cm$$ in front of a conv
Determining Index of Refraction Using Critical Angle Measurements
A student conducts an experiment to determine the index of refraction of a transparent material by m
Determining Lens Power: Experimental Measurement via Object-Image Distance
Design an experiment to determine the power of a converging lens by measuring object and image dista
Double Slit Interference Experiment: Measuring Green Light Wavelength
Design an experiment using a double slit apparatus to measure the wavelength of green light. Your de
Effect of Medium on Electromagnetic Wave Propagation: Experiment Design
Design an experiment to investigate how different media affect the propagation speed of electromagne
Effect of Medium on EM Wave Propagation: Frequency Invariance Error Analysis
A student investigates the propagation of electromagnetic waves through air with varying humidity le
Exploring the Relationship Between Frequency and Wavelength
A student conducts an experiment to examine the relationship between frequency and wavelength in dif
Frequency Calculation for Green Light
Using the provided table of wavelengths for visible light, calculate the frequency of green light an
Image Formation in a Compound Mirror System
A student investigates image formation using a compound mirror system consisting of a concave mirror
Interference and Phase Difference in Wave Superposition
Consider two coherent light waves with a constant phase difference.
Interference in Young's Double Slit Experiment
A student investigates interference patterns using a double-slit setup in a controlled laboratory ex
Interference Patterns and Young's Double Slit Experiment
An experiment using Young's double-slit setup produced the table below showing fringe positions. Ass
Investigating Snell's Law: Relationship between Incident and Refraction Angles
Design an experiment to study the relationship between the angle of incidence and the angle of refra
Measuring the Speed of Light in a Transparent Medium
A student hypothesizes that while the speed of light in a vacuum is constant ($$c = 3.0*10^{8}\, m/s
Optical Data Analysis from Spherical Mirror Measurements
An experiment is conducted where an object is placed at various distances from a concave mirror, and
Optical Fibers and Total Internal Reflection
Optical fibers use total internal reflection to guide light over long distances. Consider an optical
Optical Instrument Design: Telescope Model
A researcher is designing a simple astronomical telescope that employs a converging objective lens a
Optical Sensors in Environmental Monitoring
Environmental scientists are developing optical sensors to monitor particulate matter in water. The
Oscillating Charges and the Generation of EM Waves
An oscillating charge is a fundamental source of electromagnetic radiation. This problem involves ex
Prism Dispersion and Light Deviation
A student uses a triangular prism to study the dispersion of white light into its constituent colors
Reflection and Refraction using Snell's Law
A beam of light in air (with $$n_{air} = 1.0$$) is incident upon a glass surface (with $$n_{glass} =
Reflection and Refraction: Application of Snell’s Law
This question examines the application of Snell's law to a light beam incident on a glass surface an
Reflection and Refraction: Investigating Angle Relationships at a Glass Interface
Design an experiment to study both reflection and refraction of light at a glass-air interface. Your
Single Slit Diffraction Analysis
In this question, you will derive the condition for minima in a single slit diffraction pattern and
Single Slit Diffraction Analysis
In a single slit experiment, a diffraction pattern is recorded. A graph of intensity versus angle is
Single Slit Diffraction Analysis
A single slit with width $$a = 0.20 \text{ mm}$$ is illuminated by monochromatic light of wavelength
Single Slit Diffraction Patterns
A monochromatic light of wavelength $$λ = 600*10^{-9} \ m$$ is incident upon a single slit with a wi
Spherical Mirror Imaging: Concave Mirror Experiment
Design an experiment to verify the mirror equation for a concave mirror. Your experimental design sh
Total Internal Reflection
When light travels from water ($$n = 1.33$$) to air ($$n = 1.0$$), total internal reflection can occ
Young's Double Slit Experiment Analysis
In Young's double slit experiment, coherent light passing through two closely spaced slits produces
Young's Double-Slit Experiment Analysis
In a Young's double-slit experiment, the slit separation is $$d = 1.5*10^{-3}\,m$$, the distance to
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