Question 81: AC fundamentals

Question

When a $$d c$$ voltage of $$100 \mathrm{~V}$$ is applied to an inductor, a $$d c$$ current of $$5 \mathrm{~A}$$ flows through it. When an ac voltage of $$200 \mathrm{~V}$$ peak value is connected to inductor, its inductive reactance is found to be $$20 \sqrt{3} \Omega$$. The power dissipated in the circuit is _________ W.

Accepted Answer

To determine the power dissipated in the circuit, follow these steps:
Calculate the resistance (R) using the DC current:
$    R = \frac{100 \, 	ext{V}}{5 \, 	ext{A}} = 20 \, \Omega    $
Determine the impedance (Z) by considering both resistance (R) and inductive reactance ($X_L$):
$    Z = \sqrt{R^2 + X_L^2} = \sqrt{20^2 + (20\sqrt{3})^2} = 40 \, \Omega    $
Compute the peak current ($I_0$) using the AC peak voltage ($V_0$):
$    I_0 = \frac{V_0}{Z} = \frac{200 \, 	ext{V}}{40 \, \Omega} = 5 \, 	ext{A}    $
Calculate the power (P) using the RMS values of voltage and current, and consider the phase angle ($\cos \phi$):
$    P = V_{	ext{rms}} \cdot I_{	ext{rms}} \cdot \cos \phi = \frac{V_0 \cdot I_0}{2} 	imes \frac{R}{Z} = \frac{200 \cdot 5}{2} 	imes \frac{20}{40} = 250 \, 	ext{W}    $

AC fundamentals

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