Question

A coil of inductance 5.0 mH and negligible resistance is connected to the oscillator of the previous problem. Find the peak currents in the circuit for ω = 100 s⁻¹, 500 s⁻¹, 1000 s⁻¹.

Answer 1

Given:
Inductance of the coil, L = 5.0 mH = 0.005 H
(a) At ω = 100 s⁻¹:
Reactance of coil $\left(X_L\right)$ is given by,
X_L = $\omega L$
Here, $\omega$ = angular frequency
$\therefore$ X_L = 100 $\times$ 0.005 = 0.5 $\mathrm{\Omega }$
Peak current, I₀ = $\frac{10}{0.5}=20\mathrm{A}$
(b) At ω = 500 s⁻¹:
$$\begin{gathered} \mathrm{Reactance},X_{\mathrm{L}}=500\times \frac{5}{1000} \\ =2.5\mathrm{\Omega } \end{gathered}$$
Peak current, I₀ = $\frac{10}{2.5}=4\mathrm{A}$
(c) ω = 1000 s⁻¹:
Reactance, X_L = 1000 $\times 0.005$ = 5 $\mathrm{\Omega }$
Peak current, I₀ = $\frac{10}{5}$ = 2 A