Question

A rectangular coil of $20$ turns and area of cross-section $25sqcm$ has a resistance of $100ohm$. If a magnetic field which is perpendicular to the plane of the coil changes at the rate of $1000teslapersecond$, the current in the coil is

• A. $1.0Ampere$
• B. $50Ampere$
• C. $0.5Ampere$
• D. $5.0Ampere$

Answer 1

The correct option is C

$0.5Ampere$

Step 1: Given data:

Number of turns, $n=20$

Area of cross-section, $A=25c{m}^2=25x{10}^{-4}{m}^2$

Resistance of coil, $R=100ohm$

Change in the magnetic field, $\frac{dB}{dt}=1000teslapersecond$.

Let the current in the coil is $\begin{array}{rcl}& & i\end{array}$.

Step 2: Finding the current in the coil:

We know that,

Induced electromagnetic force $\left(emf\right)e=$Current $i\times$Load Resistance $R$

$e=iR\Rightarrow i=\frac{e}{R}$

Also electromagnetic force $\left(emf\right)e$in terms of Magnetic Field $B$ is,

$e=nA\frac{dB}{dt}$(where, $n$ is number of turns, $A$ is Area and $B$ is Magnetic Field.)

Using, $i=\frac{e}{R}$

$\begin{array}{rcl}& \Rightarrow & i=\frac{nA{\displaystyle \frac{dB}{dt}}}{R}\\ & \Rightarrow & i=\frac{20x25x{10}^{-4}x1000}{100}\\ & \Rightarrow & i=0.5Ampere\end{array}$

Hence, the current in coil is $\begin{array}{rcl}& & 0.5Ampere\end{array}$.

Hence, option C is correct.