Question

A current $I=10\sin \left(100\pi t\right)$ is passed in first coil, which induces a maximum emf of $5\pi$ volt in second coil. The mutual inductance between the coils is

• A. $10mH$
• B. $15mH$
• C. $25mH$
• D. $20mH$
• E. $5mH$

Answer 1

The correct option is D $20mH$

$I=10\sin \left(100\pi t\right)$

$\Rightarrow \frac{dI}{dt}=10\times 100\pi \cos 100nt\Rightarrow {\frac{dI}{dt}|}_{mass}=1000\pi$

we know that $\varphi =mI;m=$ mutual inductance

$\Rightarrow \frac{d\varphi }{dt}=m\frac{dI}{dt}$

$|emt|=\left|\frac{d\varphi }{dt}\right|\Rightarrow e{\frac{}{}|}_{max}=m{\frac{dI}{dt}|}_{max}$

Put $e=S\pi$ & value of ${\frac{dI}{dt}|}_{max}$

We get $m=\frac{e_{max}}{{\frac{dI}{dt}|}_{max}}=\frac{S\pi }{1000\pi }=005H$

$M=5$ mili Henry