Finding Terminal Voltage

rizardon

1. The problem statement, all variables and given/known data
In the circuit shown in the figure below the current through the 12.0V battery is measured to be 70.6 mA in the direction shown. What is the terminal voltage V_ab



2. Relevant equations
V=E-IR
I₁=I₂+I₃


3. The attempt at a solution
First I set Vab= E-IR= 24 - 10(I₁)
I₁=I₂ + I₃
So I applied Kirchoff's rule on the outer loop to find I₃
-12 - 10I₂ + 20I₃ = 0
I₃= [12 + 10I₂]/20 = 0.6000353 = 0.6A
I₁= I₂ + I₃ = 70.6 mA + 0.6A = 0.6000706A = 0.6A
V_ab= 24 -10I₁ = 24 - 6 = 18V
Is this right?

Attached Images

Circuit.bmp (96.1 KB, 26 views)

vela

What happened to the 30-ohm resistor?

The voltage due to the internal resistance of the 12-volt battery is (70.6 mA)(10 ohms) = 706 mV = 0.706 V. You seem to have divided by another factor of 1000.

rizardon

Can I combine the 20(ohm) with the 10(ohm) resistor?

vela

No, because they're neither in series nor in parallel. You could, however, combine the 20-ohm and 30-ohm resistors because they're in parallel.