# Find the difference in voltage at different points in a circuit.

1. Feb 13, 2012

### Llamas

1. The problem statement, all variables and given/known data
A section of a circuit XY shown below absorbs 50 W of power when a current I = 1.0 A passes through it as indicated by the arrow labeled i.

(a) What is the voltage difference between X and Y?
(b) What is the voltage difference across element C?

2. Relevant equations
V = IR
P = (V2)/R
P = (I2)R

3. The attempt at a solution
I have answers for both parts, but I'm not confident about them.

(a) P = V2/R
R = V/I
P = V2/(V/I) = IV
Vx= P/I = (50 W) (1.0 A) = 50 V

P = I2R
I =$\sqrt{P/R}$
Vy= IR = $\sqrt{P/R}$*R = $\sqrt{(50 W)/(2 Ω)}$*(2 Ω)
= 20V

Vx - Vy = 50 V - 20 V = 30 V

(b) Wouldn't it be 0? Why would the voltage change across the capacitor?

Edit: Maybe it's not a capacitor and I'm confused?

Thanks!

2. Feb 13, 2012

### cepheid

Staff Emeritus
C is not a capacitor. It's just some "unknown circuit element", which is why it just appears as a block. (For one thing, look up the circuit symbol for a capacitor -- it is different).

To find the voltage across C:

- You know the voltage across both.
- You can find the voltage across the 2-ohm resistor using Ohm's law
- The voltage across element C has to be the difference between the above two voltages , since they are in series. In other words, the voltage across the 2-ohm resistor and the voltage across element C have to add up to 50 V.

3. Feb 14, 2012

### Llamas

Thanks!
Vc1 = IR = (1.00 A) (2 Ω) = 2 V

Vc1 + Vc2 = 50V
2 V + Vc2 = 50 V
Vc2 = 48 V