Question 209: Electromagnetic Induction

Question

A coil of n turns and resistance $\mathrm{R} \Omega$ is connected in series with resistance $R / 4$. The combination is moved for time $t$ second through magnetic flux $\phi$ to $\phi_2$. The induced current in the circuit is

Accepted Answer

Step 1. Induced emf (FaradayÃ¢ÂÂs law):
Induced emf:
$ \mathcal{E} = n \cdot \frac{\Delta \phi}{\Delta t} = n \cdot \frac{\phi_1 - \phi_2}{t} $
(sign is not important here, they ask for current magnitude).
Step 2. Total resistance:
Coil resistance = $R$.
Extra resistance = $	frac{R}{4}$.
Total resistance $R_{	ext{eq}} = R + 	frac{R}{4} = 	frac{5R}{4}$.
Step 3. Current:
$ I = \frac{\mathcal{E}}{R_{	ext{eq}}} = \frac{n(\phi_1 - \phi_2)/t}{(5R/4)} = \frac{4 n (\phi_1 - \phi_2)}{5 R t} $
Final Answer:
$ \boxed{\; \frac{4 n (\phi_1 - \phi_2)}{5 R t} \;} $
which corresponds to
Option B
.

Answer

$\frac{2 n\left(\phi_1-\phi_2\right)}{5 R t}$

Answer

$\frac{4 n\left(\phi_1-\phi_2\right)}{5 R t}$

Answer

$\frac{3 n\left(\phi_1-\phi_2\right)}{4 R t}$

Answer

$\frac{5 n\left(\phi_1-\phi_2\right)}{3 R t}$

Electromagnetic Induction

A coil of n turns and resistance \mathrm{R} \Omega is connected in series with resistance R / 4. The combination is moved for time t second through magnetic flux \phi to \phi_2. The induced current in the circuit is

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