This problem introduces Kirchhoff\'s two rules for circuits: The figure ( Figure

Question

This problem introduces Kirchhoff's two rules for circuits:

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 readI1 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 imporant: 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).

Part B

Apply the junction rule to the junction labeled with the number 1 (at the bottom of the resistor of resistance R2).

Answer in terms of given quantities, together with the meter readings I1 and I2 and the current I3.

Part C

Apply the loop rule to loop 2 (the smaller loop on the right). Sum the voltage changes across each circuit element around this loop going in the direction of the arrow. Remember that the current meter is ideal.

Express the voltage drops in terms of Vb, I2, I3, the given resistances, and any other given quantities.

Part D

Now apply the loop rule to loop 1 (the larger loop spanning the entire circuit). Sum the voltage changes across each circuit element around this loop going in the direction of the arrow.

Express the voltage drops in terms of Vb, I1, I3, the given resistances, and any other given quantities.

Explanation / Answer

a) The junction rule describes the conservation of current in the sense that rate at which the charge flow-in is equal to its flow-out.

b) At junction 1, u get that I2 and I3 are flowing in and I1 is flowing out.So

I2 + I3 -I1 =0

c) Voltage drop across the ammeter is zero for ideal case. And if the loop is in the same direction of current through the element the voltage drop is positive.

So, starting from junction1, we get -I3*R3 +I2*R2 = 0 where V =IR

d) Starting from Junction1 in the direction of arrow, we get

Vb -I1*R1 -I3*R3 =0

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