In an alternating current circuit (frequency 50 Hz, voltage 120 V), a capacitor and a measuring device were connected

In an alternating current circuit (frequency 50 Hz, voltage 120 V), a capacitor and a measuring device were connected in series, which showed a current strength of 240 mA. What is the capacitance of a capacitor?

The AC resistance of a capacitor is determined by the formula:

Rc = ω * C, ω is the cyclic frequency, C is the capacitance.

The relationship between ω and f is given by:

f = 2 * π * ω.

Then:

ω = f / 2 * π.

Let’s write Ohm’s law for a section of the circuit:

U = I * R;

R = U / I.

Let’s substitute the expression for Rc into it:

ω * C = U / I;

C = U / I * ω.

Substitute ω:

С = U * 2 * π / I * f.

Substitute the given values:

C = 120 * 2 * π / 240 * 10 ^ (- 3) * 50 = π / 50 * 10 ^ (3) = 63 F.

Answer: the required capacitance of the capacitor will be 63 F.