How Do You Calculate Terminal Voltage Vab in a Circuit?

[rizardon]

Homework Statement

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

Homework Equations

V=E-IR
I₁=I₂+I₃

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?

 

[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.