Use Kirchhoff\'s rules to analyze the circuit in the figure below. Assume the re

Question

Use Kirchhoff's rules to analyze the circuit in the figure below. Assume the resistance values are R1 = 2100 ? and R2 = 1300 omega, and the battery emfs are 1 = 1.4 V and 2 = 3.1 V. (a) Let I1 be the branch current through R1 and I2 be the branch current through R2. Write Kirchhoff's loop rule relation for a loop that travels through battery 1, resistor 1, and battery 2. (Use the following as necessary: 1, I1, R1, 2, I2, and R2. Do not substitute numerical values, use variables only.) 0 = ________ (b) Write Kirchhoff's loop rule relation for a loop that travels through battery 2 and resistor 2. (Use the following as necessary: 1, I1, R1, 2, I2, and R2. Do not substitute numerical values, use variables only.) 0 = ________ (c) You should now have two equations and two unknowns (I1 and I2). Solve for the two branch currents. I1 = _______ A I2 = ________ A

Explanation / Answer

a) For loop one we have

E1 - I1R1 - E2 = 0

b)

E2 - I2R2 = 0

c)

1.4 - I1(2.1)-3.1 = 0

- I1(2.1) = -1.7

I1 = 0.809mA = 8.08x10-4 A

3.1 - I2(1.3) = 0

I2 = 2.385mA = 2.385x10-3 A

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