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

[Llamas]

Homework Statement

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?

Homework Equations

V = IR
P = (V²)/R
P = (I²)R

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
V_x= P/I = (50 W) (1.0 A) = 50 V

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

V_x - V_y = 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!

 

[cepheid]

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.

 

[Llamas]

Thanks!
For the second part, following your advice, I did:
V_c1 = IR = (1.00 A) (2 Ω) = 2 V

V_c1 + V_c2 = 50V
2 V + V_c2 = 50 V
V_c2 = 48 V