Question

The generator in a purely inductive AC circuit has an angular frequency of 363 rad/s. If the maximum voltage is 169 V and the inductance is 0.0937 H, what is the rms current in the circuit

Answer 1

The rms current in the circuit is 3.513 A

Step-by-step explanation:

Given;

angular frequency of the inductor, ω = 363 rad/s

maximum voltage of the inductive AC, V₀ = 169 V

Inductance of the inductor, L = 0.0937 H

Inductive reactance is given by;

`X_L = 2\pi f L= \omega L`

`X_L = 363 *0.0937\\\\X_L = 34.0131 \ ohms`

The rms voltage is given by;

`V_(rms) = (V_o)/(√(2) ) \\\\V_(rms) =(169)/(√(2) ) \\\\V_(rms) = 119.5 \ V`

The rms current in the circuit is given by;

`I_(rms) = (V_(rms))/(X_L) \\\\I_(rms) = (119.5)/(34.0131) \\\\I_(rms) = 3.513 \ A`

Therefore, the rms current in the circuit is 3.513 A