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

[Leonid92]

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.

Relevant 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?

 

[kuruman]

Posting a schematic diagram would help to avoid guesswork on our part. Thanks.

 

[Leonid92]

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]

Thank you for the schematic. I am not sure how you got R_eq. I would calculate the current in the capacitor and rheostat branches separately and then add them noting that they are not necessarily in phase with the voltage.