21.3 Kirchhoff's Rules

21.3 Kirchhoff's Rules

  • One example of dealing with multiple voltage sources is that of combinations of solar cells wired in both series and parallel combinations to yield a desired voltage and current.
    • The conversion of sunlight into electricity is done by using the photoelectric effect, in which particles of light hitting the surface of a solar cell create an electric current.
  • Most solar cells are made from pure Silicon, either as single-crystal Silicon or as a thin film of Silicon deposited upon a glass or metal backing.
    • The current output of most single cells is a function of the amount of sunlight on the cell.
    • A current of cell surface area is produced by typical single-crystal cells.
  • The solar cells are connected to the modules.
    • They can be wired in series or parallel to each other.
    • A solar-cell array or module usually has between 36 and 72 cells, with a power output of 50 W to 140 W.
  • Direct current is the output of the solar cells.
    • AC is required for most uses in a home, so a device called an inverter must be used to convert the DC to AC.
    • The extra output can be sold to the utility.
  • One can use playing cards or business cards to represent a solar cell in a virtual solar cell array.
  • The required array output can be modeled by combinations of these cards in series and parallel.
    • Each card has an output of 0.25 V and a current of 2 A.

If you were told that you only needed 18 W, what would you do?

  • There are two circuit analysis rules that can be used to analyze any circuit, simple or complex.
  • A combination of series and parallel connections is not possible.
    • Special applications of the laws of energy and charge can be used to analyze it.
  • The sum of all currents entering and leaving a junction must be the same.
  • Any changes in potential around a closed circuit path must be zero.
  • Explanations of the two rules will be given, followed by problem-solving hints for applying the rules, and a worked example that uses them.
  • The first rule requires that.
    • This can be used to solve circuit problems and analyze circuits.
  • The first rule is the application of charge, while the second rule is the application of energy.
    • The foundation of a specific application, such as circuit analysis, is formed by conservativism laws.
  • The diagram shows an example of a first rule where the sum of the currents into a junction equals the sum of the currents out of a junction.
    • The current going into the junction splits and comes out as two different currents.
    • This must be 11 A since it is 7 A and 4 A.
  • The loop rule is stated in terms of potential, rather than potential energy.
    • There are no other ways in which energy can be transferred into or out of the circuit in a closed loop.
  • The second rule requires.
    • The emf is equal to the sum of the drops in the loop.
  • An example of the second rule is where the sum of the changes in potential around a closed loop must be zero.
  • We can find the unknowns in circuits with the help of the equations we generate.
    • Currents, emfs, or resistances are unknowns.
    • An equation is produced when a rule is applied.
    • The problem can be solved if there are as many equations as unknowns.
    • There are two decisions you have to make.
    • The signs of various quantities are determined by these decisions.
  • The junction rule requires you to label the current in each branch and decide what to do with it.
    • The current will be of the correct magnitude but negative if you choose the wrong direction.
  • The loop rule requires you to identify a closed loop and decide in which direction to go around it.
    • Again, there is no risk; going around the circuit in the opposite direction reverses the sign of every term in the equation, and the following points will help you get the plus or minus signs right when applying the loop rule.
    • The emfs and the resistors go from a to b.
    • It will be necessary to build more than one loop in many circuits.
    • Consistency is needed for the sign of change in potential in each loop.
  • From a to b, each of these sources is passed through.
    • The potential changes are explained in the text.
  • The change in potential is when the current is in the same direction as the Resistor.
  • The change in potential is caused by the direction of the Resistor.
  • The change in potential is +emf when an emf is traversed from to +.
  • The change in potential is emf when an emf is traveled from + to positive charge.
  • This example shows how to find the currents.
  • The currents can't be found using the series-parallel techniques because the circuit is so complex.
    • Currents have been labeled and the figure and assumptions have been made about their directions.
    • The diagram has locations labeled with letters a through h.
  • At point a, we apply the first or junction rule.
  • It flowed into the junction and out.
    • The junction rule produces the same equation so that no new information is obtained.
    • The loop rule must be applied because this is a single equation with three unknowns.
  • The loop abcdea is considered now.
    • The change in potential is when we traverse in the same direction as the current.
    • The change in potential is when we go from b to c.
  • The internal resistance from c to d is Traversing.
    • A change in potential is given by completing the loop by going from d to a again.
  • The signs are reversed compared to the other loop because elements are in the opposite direction.
  • The three equations are sufficient to solve the three unknown currents.
  • We note that as a check.
    • The results could be checked by entering all of the values into the equation.