Question 197: Electromagnetic Induction

Question

A coil having ' $N$ ' turns and resistance ' $R$ ' $\Omega$ is connected to a galvanometer of resistance ' 6 R ' $\Omega$. The magnetic flux linked with this coil changes from $\phi_1$ weber to $\phi_2$ weber in time ' t ' second. The induced current in the circuit is

Accepted Answer

Step 1: EMF induced in coil
Magnetic flux linked with
one turn
of the coil changes from $\phi_1$ to $\phi_2$ in time $t$.
So the change of flux in
one turn
is:
$ \Delta \phi = \phi_2 - \phi_1 $
For a coil having
N turns
, total change in flux linkage is:
$ \Delta \Phi = N (\phi_2 - \phi_1) $
Hence, the
induced emf
is:
$ \mathcal{E} = \frac{\Delta \Phi}{t} = \frac{N (\phi_2 - \phi_1)}{t} $
Step 2: Equivalent resistance of circuit
The coil has internal resistance $R$.
This is connected in series with a galvanometer of resistance $6R$.
So total resistance in the circuit is:
$ R_	ext{eq} = R + 6R = 7R $
Step 3: Induced current
By OhmÃ¢ÂÂs law:
$ I = \frac{\mathcal{E}}{R_	ext{eq}} = \frac{	frac{N (\phi_2 - \phi_1)}{t}}{7R} = \frac{N(\phi_2 - \phi_1)}{7R t} $
Ã¢ÂÂ Final Answer:
Option B
:
$ \boxed{\frac{N (\phi_2 - \phi_1)}{7 R t}} $

Answer

$\frac{\mathrm{N}\left(\phi_2-\phi_1\right)}{\mathrm{t}}$

Answer

$\frac{N\left(\phi_2-\phi_1\right)}{7 R t}$

Answer

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

Answer

$\frac{N\left(\phi_2-\phi_1\right)}{6 R t}$

Electromagnetic Induction

A coil having ' N ' turns and resistance ' R ' \Omega is connected to a galvanometer of resistance ' 6 R ' \Omega. The magnetic flux linked with this coil changes from \phi_1 weber to \phi_2 weber in time ' t ' second. The induced current in the circuit is

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