Question 339: AC fundamentals

Question

When 80 volt d.c. is applied across a solenoid, a current of 0.8 A flows in it. When 80 volt a.c. is applied across the same solenoid, the current becomes 0.4 A . If the frequency of a.c. source is 50 Hz , the impedance and inductance of the solenoid is nearly

Accepted Answer

When 80 V dc is applied,
$$\begin{aligned}
& Z=\sqrt{R^2+(\omega L)^2}=R \quad \ldots(\because \omega=0 	ext { in dc circuit }) \
& Z=R=\frac{V}{I}=\frac{80}{0.8}=100 \Omega \quad \ldots 	ext { (i) }
\end{aligned}$$
When 80 V ac is applied,
$$\begin{aligned}
& Z=\frac{V}{I}=\frac{100}{0.5}=200 \Omega \quad	ext{.... (ii)}\
& Z=\sqrt{R^2+(\omega L)^2} \
& \Rightarrow(2 \pi f L)^2=Z^2-R^2 \
& L=\sqrt{\frac{200^2-100^2}{(2 \pi 	imes 50)^2}}=0.55 \mathrm{H}\quad	ext{.... [From (i) and (ii)]}
\end{aligned}$$

Answer

$200 \Omega, 0.55 \mathrm{H}$

Answer

$100 \Omega, 0.8 \mathrm{H}$

Answer

$300 \Omega, 1.2 \mathrm{H}$

Answer

$200 \Omega, 1.5 \mathrm{H}$

AC fundamentals

When 80 volt d.c. is applied across a solenoid, a current of 0.8 A flows in it. When 80 volt a.c. is applied across the same solenoid, the current becomes 0.4 A . If the frequency of a.c. source is 50 Hz , the impedance and inductance of the solenoid is nearly

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