Question

A galvanometer of resistance $50 \Omega$ giving full scale deflection for a current of 10 milliampere is to be changed into a voltmeter of range $100 \mathrm{V}$. A resistance of__________________ $\Omega$ has to be connected in series with the galvanometer.
(A) 9950
(B) 10025
(C) 10000
(D) 9975

Answer 1

Hint: We know that a galvanometer is an electromechanical instrument used for detecting and indicating an electric current. A galvanometer works as an actuator, by producing a rotary deflection in response to electric current flowing through a coil in a constant magnetic field. Galvanometer, instrument for measuring a small electrical current or a function of the current by deflection of a moving coil. The deflection is a mechanical rotation derived from forces resulting from the current.

Complete step by step answer
We know that the major significant difference between ammeter and galvanometer is that ammeter shows only the magnitude of the current. Whereas, the galvanometer shows both the direction and magnitude of the current. A galvanometer is a device that is used to detect small electric current or measure its magnitude. Some of the different types of galvanometer include Tangent galvanometer, Astatic galvanometer, Mirror galvanometer and Ballistic galvanometer.
If the south pole of the magnet is brought towards the solenoid, the galvanometer shows deflection. Current flows in the coil of the solenoid in the clockwise direction and the galvanometer shows deflection towards the left. It has a small resistance because the classical "galvanometer" involves a small coil, carrying the test current, and suspended in a strong DC magnetic field, the orientations of the field and the coil being such that a current in the coil would "torque" the coil, thereby moving the indicator needle.

Current flowing $\mathrm{I}_{\mathrm{G}}=10 \times 10^{-3} \mathrm{A}=0.01 \mathrm{A}$
Voltage range $\mathrm{V}=100$ volts
Let the resistance to be connected in series be $\mathrm{R}_{\mathrm{s}}$
Using $\mathrm{V}=\mathrm{I}_{\mathrm{G}}\left(\mathrm{R}_{\mathrm{G}}+\mathrm{R}_{\mathrm{s}}\right)$
$\therefore 100=0.01\left(50+\mathrm{R}_{\mathrm{s}}\right)$
$\Rightarrow {{R}_{s}}=9950\Omega $

So the correct answer is option A.

Note: We know that rheostat, adjustable resistor used in applications that require the adjustment of current or the varying of resistance in an electric circuit. The rheostat can adjust generator characteristics, dim lights, and start or control the speed of motors. The radial magnetic field is applied to a moving coil galvanometer to produce a constant torque on the coil. It is applied to measure the relation between the current and the angle which is non-linear such that the current cannot be measured easily.