Question

Read the two statements carefully to mark the correct option out of the options given below:

$\text{Statement -1:}$ The tangent galvanometer can be made more sensitive by increasing the number of turns of its coil.

$\text{Statement -2:}$ Current through the galvanometer is proportional to the number of turns of the coil.

• A. Both the statements are true, and the statement-$2$ is the correct explanation of statement-$1$.
• B. Both statements are true, but the statement-$2$ is not the correct explanation of the statement-$1$.
• C. The statement-$1$ true but statement-$2$ is false.
• D. The statement-$1$ is false, but statement-$2$ is true.

Answer 1

The correct option is C The statement-$1$ true but statement-$2$ is false.

Sensitivity of a tangent galvanometer is given by,
$$\text{s}=\frac{\theta }{i}\simeq \frac{\tan \theta }{i}=\frac{{\mu }_{0}N}{2a{B}_H}$$
Here,
$i\to$ Current passing through the coil
$a\to$ Radius of the coil
$B_H\to$ Horizontal component of the magnetic field
$N\to$ Number of turns of the coil
$\theta \to$ Angle of deflection

$\Rightarrow s\propto N$

So, statement-$1$ is correct.

Also, the current passing through the coil of a tangent galvanometer is given by,$$i=\left(\frac{2a{B}_H}{{\mu }_{0}N}\right)\tan \theta$$ $\Rightarrow i\propto \frac{1}{N}$

So, statement-$2$ is incorrect.

Hence, option $\left(C\right)$ is correct.