Question 330: Electromagnetic Induction

Question

A coil of $$n$$ turns and resistance $$R \Omega$$ is connected in series with a resistance $$\frac{R}{2}$$. The combination is moved for time $$t$$ second through magnetic flux $$\phi_1$$ to $$\phi_2$$. The induced current in the circuit is

Accepted Answer

When a coil of $n$ turns moves through a magnetic flux from $$\phi_1$$ to $$\phi_2$$, the emf induced in the coil is
$$	heta=-\frac{n d \phi}{d t}=\frac{-n\left(\phi_2-\phi_1ight)}{t}=\frac{n\left(\phi_1-\phi_2ight)}{t} \quad 	ext{..... (i)}$$
As, resistance $$R$$ of coil and $$\frac{R}{2}$$ are in series, so equivalent resistance is
$$R_{	ext {eq }}=R+\frac{R}{2}=\frac{3 R}{2} \quad 	ext{..... (ii)}$$
The induced current in the circuit is,
$$I=\frac{	heta}{R_{	ext {eq }}}=\frac{n\left(\phi_1-\phi_2ight)}{t\left(\frac{3 R}{2}ight)}=\frac{2 n\left(\phi_1-\phi_2ight)}{3 R t}$$

Answer

$$\frac{n\left(\phi_1-\phi_2\right)}{3 R t}$$

Answer

$$\frac{2 n\left(\phi_1-\phi_2\right)}{3 R t}$$

Answer

$$\frac{2 n\left(\phi_1-\phi_2\right)}{R t}$$

Answer

$$\frac{n\left(\phi_1-\phi_2\right)}{R t}$$

Electromagnetic Induction

A coil of $n turns and resistance R \Omega is connected in series with a resistance \frac{R}{2}. The combination is moved for time t second through magnetic flux \phi_1 to \phi_2$. The induced current in the circuit is

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