Question 293: AC fundamentals

Question

A resistance of $200 \Omega$ and an inductor of $\frac{1}{2 \pi} \mathrm{H}$ are connected in series to a.c. voltage of 40 V and 100 Hz frequency. The phase angle between the voltage and current is

Accepted Answer

Given:
Resistance, $R = 200\ \Omega$
Inductance, $L = \dfrac{1}{2\pi}\ \mathrm{H}$
Frequency, $f = 100\ \mathrm{Hz}$
Voltage, $V = 40\ \mathrm{V}$
For an $R$-$L$ series circuit, the phase angle $\phi$
by which the current lags the voltage
is given by:
$$ 	an\phi = \frac{X_L}{R} $$
where $X_L$ is the inductive reactance.
Step 1:
Calculate $X_L$
$ X_L = 2\pi f L = 2\pi 	imes 100 	imes \frac{1}{2\pi} = 100\ \Omega $
Step 2:
Calculate the phase angle
$ 	an\phi = \frac{X_L}{R} = \frac{100}{200} = 0.5 $
$ \phi = 	an^{-1}(0.5) $
Step 3:
Check options
Option D: $	an^{-1}(0.5)$
So, the correct answer is
$ \boxed{ 	ext{Option D: } 	an^{-1}(0.5) } $

Answer

$	an ^{-1}(1 / 5)$

Answer

$	an ^{-1}(1 / 4)$

Answer

$	an ^{-1}(1 / 3)$

Answer

$	an ^{-1}(0.5)$

AC fundamentals

A resistance of 200 \Omega and an inductor of \frac{1}{2 \pi} \mathrm{H} are connected in series to a.c. voltage of 40 V and 100 Hz frequency. The phase angle between the voltage and current is

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