Assume the resistance values are R 1 = 2,100 %u03A9 and R 2 = 1,150 %u03A9 , and

Question

Assume the resistance values are R1 = 2,100 %u03A9 and R2 = 1,150 %u03A9, and the battery emfs are emf1 = 1.3 V and emf2 = 3.5 V.

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

(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. (Assume the current in the loop flows clockwise in the positive direction. Use the following as necessary: emf1, I1, R1, and emf2. 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. (Assume the current in the loop flows clockwise in the positive direction. Use the following as necessary: emf2, 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.

Explanation / Answer

Loop 1: -E1+R1*I1+E2=0 Loop 2: -E2+R2*I2=0 I2=E2/R2 given E1=1.3 V E2=3.5 V R1=2100 ohms R2= 1150 ohms I1=(E1-E2)/R1 I1= (1.3-3.5)/2100 = -0.00104 Amps I2=E2/R2 I2=3.5/1150 = 0.00304 Amps

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