In the part of an a.c. circuit as shown, the resistance $\mathrm{R}=0.2$ $\Omega$. At a certain instant…
In the part of an a.c. circuit as shown, the resistance $\mathrm{R}=0.2$ $\Omega$. At a certain instant $\left(\mathrm{V}_{\mathrm{A}}-\mathrm{V}_{\mathrm{B}}\right)=0.5 \mathrm{~V}, \mathrm{I}=0.5 \mathrm{~A}$ and $\frac{\Delta \mathrm{I}}{\Delta \mathrm{t}}=8 \mathrm{~A} / \mathrm{s}$. The inductance of the coil is
$0.04 \mathrm{H}$
$0.02 \mathrm{H}$
$0.08 \mathrm{H}$
$0.05 \mathrm{H}$
Solution
In the part of an a.c. circuit
$\begin{aligned}
& V_A-V_B=L \frac{d I}{d t}+I R \\
& 0.5=8 L+0.5 \times 0.2 \\
& \therefore 8 L=0.4 \\
& \therefore L=\frac{0.4}{8}=0.05 \mathrm{H}
\end{aligned}$
.
