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

Answer:

The rms current in the circuit is 3.513 A

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;

$V_{rms} = \frac{V_o}{\sqrt{2} } \\\\V_{rms} =\frac{169}{\sqrt{2} } \\\\V_{rms} = 119.5 \ V$

The rms current in the circuit is given by;

$I_{rms} = \frac{V_{rms}}{X_L} \\\\I_{rms} = \frac{119.5}{34.0131} \\\\I_{rms} = 3.513 \ A$

Therefore, the rms current in the circuit is 3.513 A