Question 315: AC fundamentals

Question

When 100 V d.c. is applied across a solenoid, a current of 1 A flows in it. When 100 a.c. is applied across it, the current drops to 0.5 A. If the frequency is 50 Hz , the impedance and inductance is

Accepted Answer

For D.C., $R=\frac{100}{1}=100 \Omega$
For A.C., $Z=\frac{100}{0.5}=200 \Omega$
Now, $\mathrm{Z}^2=\mathrm{R}^2+\mathrm{X}_{\mathrm{L}}^2$
$$\begin{aligned}
	herefore\quad \mathrm{X}_{\mathrm{L}}^2 & =(200)^2-(100)^2 \
& =40000-10000=30000 \
	herefore\quad\mathrm{X}_{\mathrm{L}} & =\sqrt{30000}=100 \sqrt{3} \Omega \
\mathrm{X}_{\mathrm{L}} & =2 \pi \mathrm{fL} \
	herefore\quad\mathrm{~L} & =\frac{\mathrm{X}_{\mathrm{L}}}{2 \pi \mathrm{f}}=\frac{100 \sqrt{3}}{2 	imes \pi 	imes 50} \
& =\frac{\sqrt{3}}{\pi} \mathrm{H}
\end{aligned}$$

Answer

$200 \Omega, \sqrt{3} / \pi \mathrm{H}$

Answer

$100 \Omega, \sqrt{3} \mathrm{H}$

Answer

$200 \Omega, 1 \mathrm{H}$

Answer

$100 \Omega, 1 \mathrm{H}$

AC fundamentals

When 100 V d.c. is applied across a solenoid, a current of 1 A flows in it. When 100 a.c. is applied across it, the current drops to 0.5 A. If the frequency is 50 Hz , the impedance and inductance is

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