Question 206: 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

Step 1: Induced emf
Induced emf across $n$ turn coil:
$ \mathcal{E} = n \frac{\Delta \phi}{\Delta t} = n \frac{\phi_1 - \phi_2}{t} $
Step 2: Total resistance of the circuit
Self resistance of coil = $R$.
External resistance = $	frac{R}{2}$.
Total resistance:
$ R_{	ext{total}} = R + \frac{R}{2} = \frac{3R}{2}. $
Step 3: Induced current
$ I = \frac{\mathcal{E}}{R_{	ext{total}}} = \frac{n(\phi_1 - \phi_2)/t}{	frac{3R}{2}} = \frac{2 n (\phi_1 - \phi_2)}{3 R t}. $
Final Answer:
$ \boxed{	ext{Option B: } \frac{2n(\phi_1 - \phi_2)}{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

$\frac{\mathrm{n}\left(\phi_1-\phi_2\right)}{\mathrm{Rt}}$

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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