Question

A galvanometer of resistance $50\Omega$ is connected to a battery of $3V$ along with a resistance of $2950\Omega$ in series. A full-scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce this deflection to 20 divisions, the resistance in series should be:
(A). $6050\Omega$
(B). $4450\Omega$
(C). $5050\Omega$
(D). $5550\Omega$

Answer 1

A galvanometer is used to detect current in a circuit. It allows very little current to flow through it. When we increase the resistance in a circuit the current decreases, therefore, according to ohm’s law, resistance is related to the potential in the circuit and current in the circuit.
Formulas used:
$R=\dfrac{V}{I}$

Complete step-by-step solution:
Given, the total resistance in the circuit is
$\begin{aligned} & R'=R+G \\\ & \Rightarrow R'=2950+50 \\\ & \therefore R'=3000\Omega \\\ \end{aligned}$
Here, $R$ is the resistance connected in series
$G$ is the resistance of galvanometer
By ohm’s law, we have,
$R=\dfrac{V}{I}$
Here,
$R$ is the total resistance in the circuit
$V$ is the potential in the circuit
$I$ is the current in the circuit
Given, $V=3V$. In the above equation of ohm’s law, we substitute given values to get,
$\begin{aligned} & 3000=\dfrac{3}{I} \\\ & \Rightarrow I=\dfrac{3}{3000} \\\ & \therefore I=1mA \\\ \end{aligned}$
The value of current $I=1mA$ corresponds to 30 divisions on the galvanometer. Current which corresponds to 1 division of the galvanometer is $I'=\dfrac{1}{30}mA$. Therefore, the current corresponding to 20 divisions only will be-
$\begin{aligned} & I''=\dfrac{1}{30}\times 20mA \\\ & \Rightarrow I''=\dfrac{2}{3}mA \\\ \end{aligned}$
For current corresponding to 20 divisions flowing in the circuit, the new resistance will be-
Using the equation of ohm’s law, we get,
$\begin{aligned} & r+50=\dfrac{3}{\dfrac{2}{3}\times {{10}^{-3}}} \\\ & \Rightarrow r+50=\dfrac{9000}{2} \\\ & \Rightarrow r=4500-50 \\\ & \therefore r=4450\Omega \\\ \end{aligned}$
Therefore, the resistance in the circuit to be connected in series so that deflections in the galvanometer is only till 20 divisions is $4450\Omega$. Hence, the correct option is (B).

Note: Galvanometer is originally used to detect current in a circuit but it can also be used as an ammeter by connecting a high magnitude resistance in series with the galvanometer. It can also be converted to a voltmeter by connecting a low resistance in parallel to the galvanometer. In the galvanometer, the deflections produced for unit current is called its current sensitivity and the deflection produced per unit voltage is called its voltage sensitivity.