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

19.2 mA

Step-by-step explanation:

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

L = 16 H

f = 60 Hz

Vrms = 116 V

`X_(L)=2* \pi * f* L`

`X_(L)=2* 3.14 *  60 * 16`

XL = 6028.8 ohm

`X_(C)=(1)/(2 * \pi  * f * C)`

`X_(C)=(1)/(2* 3.14  * 60 * 9 * 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)=(V_(rms))/(Z)`

`I_(rms)=(116)/(6036)`

Irms = 0.0192 A

Irms = 19.2 mA