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The generator in a purely inductive AC circuit has an angular frequency of 553 rad/s. If the maximum voltage is 222 V and the inductance is 0.102 H, what is the rms current in the circuit? Answer in units of A

Answer :

onyebuchinnaji

Answer:

The rms current is 2.78 A

Explanation:

Given;

angular frequency, ω = 553 rad/s

maximum voltage, V₀ = 222 V

inductance, L = 0.102 H

The inductive reactance is given by;

[tex]X_l = \omega L\\\\X_l = 553 *0.102\\\\X_l = 56.406 \ ohms[/tex]

The root mean square voltage is given by;

[tex]V_{rms} = 0.7071 \ V_o\\\\V_{rms} = 0.7071 * 222\\\\V_{rms} = 156.976 \ V[/tex]

The rms current is given by;

[tex]I_{rms} = \frac{V_{rms}}{X_l} \\\\I_{rms} = \frac{156.976}{56.406}\\\\ I_{rms} = 2.78 \ A[/tex]

Therefore, the rms current is 2.78 A

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