21.1 Resistors in Series and Parallel

21.1 Resistors in Series and Parallel

• The convention for determining the correct signs of various terms is used in the analysis of a complex circuit.

• Explain why a voltmeter must be connected to the circuit.

• A diagram showing an ammeter in a circuit is needed.

• Explain how a galvanometer can be used.

• The resistance must be placed in a series with a galvanometer to allow it to be used as a voltmeter.

• Measuring the voltage or current in a circuit can never be exact.

• A null measurement device is more accurate than a standard ammeter.

• A Wheatstone bridge can be used to calculate resistance in a circuit.

• Explain the importance of the time constant, t, and calculate the time constant for a given resistance.

What happens to a graph of the voltage across aCapacitor over time as it charges

• Explain how a timing circuit works.

• Determine the speed of a strobe flash needed to stop the movement of an object.

• There are electric circuits.
• There are some that are simple.

• The topic of electric circuits is taken a step further in this collection of modules.
• Everything in this module applies to both DC and AC.
• Matters become more complicated when they are involved.
• Capacitors and other nonresistive devices with AC are left for a later chapter when we consider what happens when they are connected to DC voltage sources.
• This chapter covers a number of important DC instruments, such as meters that measure voltage and current.

• The total resistance of a combination depends on how they are connected.

• It makes sense that the total resistance is the sum of the individual resistances, since the current has to pass through each resistance in a sequence.

• Three resistors are connected to a battery.

• Another way to think of this is that the voltage is needed to make a current flow through a resistance.

• The equation is based on energy and charge.
• The electrical potential energy can be described by the equation.

• The laws of energy and charge are the basis of the expressions for series and parallel resistance.
• The general behavior and effects of electricity are explained by the two laws that are directly involved in electrical phenomena.

• There is no other source for the energy in the circuit.
• As stated, the charge cancels.

• The total or equivalent series resistance of three resistors is implied.

• Since all of the current must pass through each Resistor, the resistance of each Resistor adds up.

• Ohm's law gives the voltage or drop-in a Resistor.

• The same full current is flowing through each Resistor.

• The power can be calculated by where the voltage drops across the resistor, not the full voltage of the source.
• The values will be the same.

• The easiest way to calculate the power output of the source is to use the source's voltage.

• The total power dissipated by the resistors is the same as the power put out by the source.

• To conserve energy, the power output of the source needs to be the same as the total power dissipated by the resistors.

• 2 are added by series resistances.

• Individual resistors don't get the total source voltage, but they do divide it.

• When the wires are connected with negligible resistance, the Resistors are in parallel.
• The source's full voltage is applied to each Resistor.

• If the voltage source was not overloading, the resistors would draw the same current.
• For example, an automobile's headlights, radio, and so on, are wired in parallel so that they can operate independently.
• In your house, or any building, the same is true.

• Let's consider the currents that flow and how they are related to resistance to find an expression for the parallel resistance.

• The last two equations have the same terms inside their parentheses.

• The total resistance is less than the smallest of the individual resistances.

• The total resistance is lower when the resistors are connected in parallel because more current flows from the source than would flow for any of them individually.

• The total resistance is found using the equation below.

• To find the total resistance, we must invert this.

• The total resistance can be found from the total current.

• Current for each device is larger than for the same devices connected in a series.
• A circuit with parallel connections has a smaller total resistance than a series circuit.

• The individual currents can be calculated from the Ohm's law.

• This is consistent with the way charge is handled.

• Since all three of the equations relating power to current, voltage, and resistance are known, the dissipated power can be found using any of them.
• Let us use since the resistors get full voltage.

• When connected in series to the same voltage source, the power dissipated by each Resistor is lower.

• There are many ways in which the total power can be calculated.

• This is in line with the law of energy saving.

• The currents and powers in parallel connections are more powerful than in the same devices in series.

• Parallel resistance is smaller than any individual resistance in the combination.

• The source's full voltage is applied to each of the parallel Resistors.

• The parallel resistors divide the current.

• A lot of the connections of the resistors are just combinations of series and parallel.
• When wire resistance is considered, these are often encountered.
• In that case, wire resistance is in a series with other resistances.

• The technique illustrated in arious parts can be used to reduce combinations of series and parallel to a single equivalent resistance until a single resistance is left.
• The process takes more time than it should.

• There are both series and parallel parts in this combination.
• Each is reduced until a single equivalent resistance is reached.

• It could be the resistance of wires from a car battery to its electrical devices.

• The next example shows how important wire resistance is when it is not negligible.

• The resistors from the previous two examples were wired in a different way.

• The combination of these three resistors is connected to a voltage source so that they are in parallel with one another.

• The full current flows through to find the drop in.

• Ohm's law is used to find the total current.

• The applied voltage is less than the total.

• We need to find the voltage applied to it to find the current.
• The voltage is applied to a parallel combination of resistors.

• The current is less than the one that flowed through when it was connected in parallel to the battery.

• When connected to the 12.0-V source, the power is less than the 24.0 W dissipated.

• One implication of this last example is that resistance in wires reduces the power that is delivered.
• This loss can be significant if the wire resistance is relatively large.
• The drop in the wires can be significant if a large current is drawn.

• The refrigerator light dims when you are rummaging in it and the motor is on.

• You can see the passenger compartment light dim when you start the engine of your car, although this may be due to resistance inside the battery itself.

• A large current flows when the device is switched on because it has a very low resistance.
• This increased current causes a larger drop in the wires, which causes the light bulb to dim noticeably.

• The answer is that the large current the appliance motor draws causes a significant drop in the wires.

• If you can draw a circuit diagram of the resistors that can't be broken down into parallel and series combinations, that's great.

• There are many ways to connect resistors that are not combinations of series and parallel.
• You will be able to analyze the circuit if the rules are introduced in such cases.