Question

A range of galvanometer is V when 50ohm of resistance is connected in series. Its range gets doubled when 500 ohms of resistance are connected in series. Galvanometer resistance is:
A. 100 ohm
B. 200 ohm
C. 300 ohm
D. 400 ohm

Answer 1

Hint: A galvanometer is an electrical instrument that detects the presence of current in the circuit. A galvanometer is a sensitive electromagnetic device that can measure low currents even of the order of a few microamperes. It consists of metal pieces on which wire is wound and magnet field is applied, due to which it gets rotated on passing even the smallest current.

Formula used: $V=I_g(x+R)$

Complete step-by-step solution:
The range of the galvanometer is defined by the amount of current it can measure. By arranging the value of resistance, we can adjust its range.
Let the Galvanometer resistance be ‘x’.
Also, let the current flowing through the galvanometer be $I_g$, hence using ohm’s law, we can write;
$V=I_g(x+R)$, where R is the external resistance.
Given R= 50 ohm and the Galvanometer range with this resistance is V.
Thus, $V=I_g(x+50)$ ……………….... ①
Also, if R= 500 ohm, Range becomes ‘2V’ (given).
Thus, $2V = I_g(x+500)$ ...............②
Now, dividing ② and ① we get
$2 = \dfrac{x+500}{x+50}$
Or $2x+100=x+500$
Or $x=400 ohm$
Hence, ‘x’ which we assumed to be galvanometer resistance comes out to be 400 ohms, option D is correct.

Note: A galvanometer is used to detect the presence of current in the circuit. It can be of many types. Some of them are tangent galvanometer, mirror galvanometer, astatic galvanometer, ballistic galvanometer, and moving coil galvanometer. The most important and widely used galvanometer is the moving coil galvanometer.