# Determine the effective current value in the circuit with C and R

## Homework Statement:

The rheostat and capacitor bank are connected in parallel and connected to a sinusoidal voltage source of 220 V with a frequency of 50 Hz. The resistance of the rheostat is 20 Ohm, the capacitance of the capacitor bank is 100 μF. Determine the effective current value in the unbranched part of the circuit.

## Homework Equations:

1) Xc = 1/(ω*C) = 1/(2*π*f*C)
2) I = U/resistance
Given:
U = 220 V
f = 50 Hz
r = 20 Ohm
C = 100 μF
Find: I
Solution:
1) Xc = 1/(ω*C) = 1/(2*π*f*C) = 1/(2*π*50*10^-4) = 31.83 Ohm
2) R_eq - equivalent resistance
R_eq = (r*Xc)/(r+Xc) = (20*31.83)/(20+31.83) = 12.28 Ohm
3) I = U/R_eq = 220/12.28 = 17.9 A

True answer given in the textbook is 13 A.

Could you please tell, what is wrong in the solution?

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kuruman
Homework Helper
Gold Member
Posting a schematic diagram would help to avoid guesswork on our part. Thanks.

Posting a schematic diagram would help to avoid guesswork on our part. Thanks.
A schematic diagram is not given in the problem statement. I attached a sheme drawn on my own.

kuruman
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