I need help calculating currents in a circuit with resistors. If anyone could he

Question

I need help calculating currents in a circuit with resistors. If anyone could help me, I would really appreciate it if you could go through the problem and write down the work. Thanks!

Note: the answers to (a) and (b) will be the solution to a set of simultaneous equations; use junction and loop equations as necessary. In this situation one of the currents is known, but one battery emf is not. In the circuit shown below, the current in the middle branch is measured to be 50.0 mA in the direction indicated. (a) Find the current through the 1.00 resistor and indicate its direction (right or left) (b) What is the emf e of the battery in the middle branch? (c) For the loop containing both batteries, draw a qualitative graph of potential V vs. location in the loop (similar to figure 25.20 on page 833 of the text), starting and ending at point B and moving clockwise (assume the negative terminal of the 1.20 V battery is grounded) 1.00 1.20 V 50.0 mA 5.00 2.00 4.00

Explanation / Answer

apply KVl to the left loop

e-(2*50*10^-3)-5*i1 = 0

e = (0.1)+(5*i1).........(1)

and to the right loop

(1*i2)+1.2+(4*i2)+(2*50*10^-3)-e = 0

e = (5*i2)+1.3...........(2)

at junction A

i1+i2 = 50*10^-3 A...(3)

from (1) and (2)

5i1 - 5i2 = 1.2 ......(4)

solving( 3) and (4)

10*i1 = 1.45

i1 = 0.145 A

i2 = 0.05-0.145 = -0.095 A = -95 mA

A) current through 1 ohm is 95 mA from left to right

B) e = -(5*0.095)+1.3 = 0.825 V

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