# Physics II Pearson Chapter 23

Draw a circuit diagram for the circuit of the figure.
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Learning Goal:
To understand the origins of both of Kirchhoff's rules and how to use them to solve a circuit problem.

This problem introduces Kirchhoff's two rules for circuits:
Kirchhoff's loop rule: The sum of the voltage changes across the circuit elements forming any closed loop is zero.
Kirchhoff's junction rule: The algebraic sum of the currents into (or out of) any junction in the circuit is zero.

The figure (Figure 1) shows a circuit that illustrates the concept of loops, which are colored red and labeled loop 1 and loop 2. Loop 1 is the loop around the entire circuit, whereas loop 2 is the smaller loop on the right. To apply the loop rule you would add the voltage changes of all circuit elements around the chosen loop. The figure contains two junctions (where three or more wires meet)--they are at the ends of the resistor labeled R3. The battery supplies a constant voltage Vb, and the resistors are labeled with their resistances. The ammeters are ideal meters that read I1 and I2 respectively.

The direction of each loop and the direction of each current arrow that you draw on your own circuits are arbitrary. Just assign voltage drops consistently and sum both voltage drops and currents algebraically and you will get correct equations. If the actual current is in the opposite direction from your current arrow, your answer for that current will be negative. The direction of any loop is even less important: The equation obtained from a counterclockwise loop is the same as that from a clockwise loop except for a negative sign in front of every term (i.e., an inconsequential change in overall sign of the equation because it equals zero).

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Consider the circuit shown in the figure.

a. What are the magnitude and direction of the current in the 20 Ω resistor in (Figure 1)?
b. Select the correct graph of the potential as a function of the distance traveled through the circuit, traveling clockwise from the lower left corner, where V = 0 V. Assume the elements are connected by ideal wires.