Question

A galvanometer coil has a resistance of $150\Omega$ gives full-scale deflection for a current of $4mA$. To convert it to an ammeter of range $0$ to $6A$

• A. $10m\Omega$ resistance is to be connected in parallel to the galvanometer.
• B. $10m\Omega$ resistance is to be connected in series to the galvanometer.
• C. $0.1\Omega$ resistance is to be connected in parallel to the galvanometer.
• D. $0.1\Omega$ resistance is to be connected in series to the galvanometer.

Answer 1

Answer: (C)

$0.1\Omega$ resistance is to be connected in parallel to the galvanometer.

Given: A galvanometer having a coil resistance of $150\Omega$ shows full scale deflection when current of $4mA$ passes through it

To find when can it be converted into an ammeter of range $0$ to $6A$

Solution:

Galvanometer is a very sensitive instrument therefore it cannot measure heavy currents. In order to convert a Galvanometer into an Ammeter, a very low shunt resistance is connected in parallel to Galvanometer. Value of shunt is so adjusted that most of the current passes through the shunt.

If resistance of galvanometer is $R_g$ and it gives full-scale deflection when current $I_g$ is passed through it. Then,

$V=I_g{R}_g⟹V=4\times {10}^{-3}A\times 150\Omega$

Let a shunt of resistance ($R_s$) is connected in parallel to galvanometer. If total current through the circuit is $I$.

$I=6A=I_s+I_g$

$V=I_s{R}_s=(I-I_g)R_s$

$(I-I_g)R_s=I_g{R}_g$

$(6-4\times {10}^{-3})R_s=150\times 4\times {10}^{-3}⟹R_s=0.1\Omega$

is the resistance that should be connected in parallel to convert it into an ammeter of range $6A$.