Question

A 9 µF capacitor and a 16 H inductor are connected in series with a 60 Hz source whose rms output is 116 V. Find the rms current in the circuit. Answer in units of mA.

Answer 1

Answer:

19.2 mA

Explanation:

C = 9 micro farad = 9 x 10^-6 F

L = 16 H

f = 60 Hz

Vrms = 116 V

$X_{L}=2\times \pi \times f\times L$

$X_{L}=2\times 3.14 \times 60 \times 16$

XL = 6028.8 ohm

$X_{C}=\frac{1}{2 \times \pi \times f \times C}$

$X_{C}=\frac{1}{2\times 3.14 \times 60 \times 9 \times 10^{-6}}$

Xc = 294.88 ohm

Let Z be the impedance of the circuit.

$Z=\sqrt{X_{L}^{2}+X_{C}^{2}}$

$Z=\sqrt{6028.8^{2}+294.88^{2}}$

Z = 6036 ohm

$I_{rms}=\frac{V_{rms}}{Z}$

$I_{rms}=\frac{116}{6036}$

Irms = 0.0192 A

Irms = 19.2 mA