Question

Two coils, held in fixed position have a mutual inductance of 70 μH, one coil carries current $50sin\left(100\pi t\right)$ and other coil has resistance $8\pi$ $\Omega$, find peak current in other coil.

• A. $\frac{7}{160}$ A
• B. $\frac{3}{160}$ A
• C. $\frac{5}{160}$ A
• D. $\frac{9}{160}$ A

Answer 1

The correct option is A $\frac{7}{160}$ A

$emf=M\frac{di}{dt}$
$i=\frac{e}{R}=\frac{d\varphi /dT}{R}=\frac{d\left(Mi\right)/dt}{R}=\frac{M.di/dt}{R}$
$=\frac{70\times {10}^{-6}}{8\pi }=\frac{d}{dt}\left(i_{0}sinwt\right)$
$=\frac{70\times {10}^{-6}}{8\pi }=\left(i_0\right)wcoswt$
$i_{peak}=\frac{70\times {10}^{-6}}{8\pi }\times 50\times 100\pi$
$=\frac{7\times 5\times {10}^{-2}}{8}=\frac{35}{800}=\frac{7}{160}$ A