The total impedance of an RC circuit with a resistance of 200 Ω is 1060 Ω. If the frequency of the applied voltage is 20.0 Hz, what is the value of the capacitance in this circuit?
A) 6.64 μF
B) 7.64 μF
C) 8.64 μF
D) 9.64 μF
E) 200 μF

Question

Quizplus · Accepted Answer

The total impedance of an RC circuit is given by:

|Z| = √(R^2 + Xc^2)

where R is the resistance and Xc is the reactance of the capacitor, which is given by:

Xc = 1/(2πfC)

where f is the frequency and C is the capacitance.

Substituting the given values, we have:

1060 = √(200^2 + (1/(2πx20xC))^2)

Solving for C gives:

C = 7.64 μF (rounded to two decimal places)

Therefore, the correct answer is B.

The Total Impedance of an RC Circuit with a Resistance