Question

An RC circuit consists of a 20.0 Hz, 16.0 V source producing a 2.00 mA current when connected to a capacitor. What is the capacitance?

a) 4.0 F
b) 8.0 F
c) 10.0 F
d) 12.0 F

Answer 1

To find the capacitance of a capacitor in an RC circuit with a 20.0 Hz, 16.0 V source and a 2.00 mA current, one must calculate the capacitive reactance using Ohm's law and then use it to solve for capacitance. The correct answer is 10.0 F.

Step-by-step explanation:

The student has asked about calculating the capacitance of a capacitor connected to a 20.0 Hz, 16.0 V source which produces a 2.00 mA current. To solve for capacitance (C), we use the formula for capacitive reactance (Xc), which is Xc = 1/(2πfC), where f is the frequency and Xc is the reactance.

First, we must calculate the reactance by using Ohm's law (V = IX), where V is voltage and I is current, thus Xc = V/I. After calculating reactance, we rearrange our first formula to solve for capacitance, C = 1/(2πfXc).

Given:
V = 16.0 V
I = 2.00 mA = 0.002 A
f = 20.0 Hz

First, calculate Xc:
Xc = V/I
Xc = 16.0 V / 0.002 A
Xc = 8000 Ω.

Now, calculate C:
C = 1/(2πfXc)
C = 1/(2π(20.0 Hz)(8000 Ω))
C = ≈ 10.0 F

Therefore, the correct answer is (c) 10.0 F.