Question 282: AC fundamentals

Question

An ideal inductor of $\left(\frac{1}{\pi}\right) \mathrm{H}$ is connected in series with a $300 \Omega$ resistor. If a $20 \mathrm{~V}, 200 \mathrm{~Hz}$ alternating source is connected across the combination, the phase difference between the voltage and current is

Accepted Answer

Given:
Inductor: $L = 	frac{1}{\pi} \, 	ext{H}$
Series resistor: $R = 300 \,\Omega$
AC source: $V = 20 \,	ext{V}, \, f = 200 \,	ext{Hz}$
Step 1: Compute Inductive Reactance
$ X_L = 2 \pi f L $
$ = 2 \pi \cdot 200 \cdot 	frac{1}{\pi} $
$ = 400 \,\Omega $
Step 2: Phase Angle
For an RL circuit in series, the phase angle between voltage and current is
$ \phi = 	an^{-1}\left(\frac{X_L}{R}ight) $
$ = 	an^{-1}\left(\frac{400}{300}ight) $
$ = 	an^{-1}\left(\frac{4}{3}ight) $
Final Answer:
The phase difference is:
Option B: $\;	an^{-1}\!\left(	frac{4}{3}ight)$
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Answer

$	an ^{-1}\left(\frac{3}{4}ight)$

Answer

$	an ^{-1}\left(\frac{4}{3}ight)$

Answer

$	an ^{-1}\left(\frac{5}{4}ight)$

Answer

$	an ^{-1}\left(\frac{4}{5}ight)$

AC fundamentals

An ideal inductor of \left(\frac{1}{\pi}\right) \mathrm{H} is connected in series with a 300 \Omega resistor. If a 20 \mathrm{~V}, 200 \mathrm{~Hz} alternating source is connected across the combination, the phase difference between the voltage and current is

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