Question

A galvanometer with a scale divided into 100 equal divisions has a current sensitivity of 10 divisions per milliampere and a voltage sensitivity of 2 divisions per millivolt. The galvanometer resistance will be
(a)$4\Omega$
(b)$5\Omega$
(c)$3\Omega$
(d)$7\Omega$

Answer 1

In order to solve this question, we need to have the knowledge and formula used below about the moving coil galvanometer as well as sensitivity. So,
From the question, given:
Current sensitivity $= 10{\text{ }}div/mA$ and there are $100$ divisions on the scale.

Complete step-by-step answer:
Current required for full scale deflection.
${I_g} = \dfrac{1}{{10}} \times 100mA = 10mA = 0.1A$
Also, voltage sensitivity $= 2{\text{ }}div/mV$
voltage required for full scale deflection,
${V_g} = \dfrac{1}{2} \times 100mV = 0.05V$
Galvanometer resistance is given by,
$G = \dfrac{{{V_g}}}{{{I_g}}} = \dfrac{{0.05}}{{0.01}} = 5\Omega$

Hence, the correct answer to the question is option (b).

Additional Information: A moving coil galvanometer is an instrument which is used to measure electric currents. It is a sensitive electromagnetic device which can measure low currents even of the order of a few microamperes. Torque acts on a current-carrying coil suspended in the uniform magnetic field. Due to this, the coil rotates. Hence, the deflection in the coil of a moving coil galvanometer is directly proportional to the current flowing in the coil.It consists of a rectangular coil of a large number of turns of thinly insulated copper wire wound over a light metallic frame.

Note: While solving this question, we should be aware of the different types of formula used here. Also some of the basic knowledge about the galvanometer is must. Especially how the different values of the variable of the formula is used from the question. The formula is modified and used here to take out the required solution for the problem given here.