Question

A moving coil ammeter requires a potential difference of 0.4V across it for full scale deflection. It has fixed shunt resistance 0.01 ohm with a coil circuit resistance of R=1k ohm. The value of shunt required to give full scale deflection when the total current is 10A is equal to.
A) 0.02 ohm.
B) 0.04 ohm.
C) 0.05 ohm.
D) 0.06 ohm.

Answer 1

Hint: A moving coil ammeter consists of a coil which can move freely between the two poles of the permanent magnet also the coil starts deflecting at a certain angle which current passes through the coil. A shunt is a device which provides a low resistance path which helps the current to pass from one point to another point.


Formula Used:
The formula of the shunt resistance is given by,
${R_{sh}} = \dfrac{{{I_g} \cdot R}}{{I - {I_g}}}$
Where shut resistance is ${R_{sh}}$ the full scale deflection current is ${I_g}$ the current through the circuit is $I$ and resistance of the coil is$R$.
The formula of full scale deflection current is given by,
${I_g} = \dfrac{V}{R}$
Where the full scale deflection current is ${I_g}$ the potential difference is $V$ and the resistance of the coil is equal to $R$.

Complete step by step answer:
It is given in the problem that a moving coil ammeter requires a potential difference of 0.4V across it for full scale deflection. It has fixed shunt resistance 0.01 ohm with a coil circuit resistance of R=1k ohm if the total current is 10A then we need to find the shunt resistance for full scale deflection.
First of all let us calculate the full scale deflection current. The formula of full scale deflection current is given by,
${I_g} = \dfrac{V}{R}$
Where the full scale deflection current is ${I_g}$ the potential difference is $V$ and the resistance is equal to$R$.
The R=1k ohm and the potential difference is 0.4V, therefore the full deflection current will be,
$ \Rightarrow {I_g} = \dfrac{V}{R}$
$ \Rightarrow {I_g} = \dfrac{{0 \cdot 4}}{{{{10}^3}}}$
$ \Rightarrow {I_g} = 0 \cdot 4 \times {10^{ - 3}}A$………eq. (1)
Now let us calculate the shunt resistance. The formula of the shunt resistance is given by,
${R_{sh}} = \dfrac{{{I_g} \cdot R}}{{I - {I_g}}}$
Where shut resistance is ${R_{sh}}$ the full scale deflection current is ${I_g}$ the current through the circuit is $I$ and resistance of the coil is$R$.
As the value of full scale deflection current is equal to ${I_g} = 0 \cdot 4 \times {10^{ - 3}}A$ from equation (1) the total current is 10A the coil resistance is equal to 1k ohm then the value of the shunt resistance is equal to,
$ \Rightarrow {R_{sh}} = \dfrac{{{I_g} \cdot R}}{{I - {I_g}}}$
$ \Rightarrow {R_{sh}} = \dfrac{{\left( {0 \cdot 4 \times {{10}^{ - 3}}} \right) \cdot \left( {{{10}^3}} \right)}}{{10 - \left( {0 \cdot 4 \times {{10}^{ - 3}}} \right)}}$
$ \Rightarrow {R_{sh}} = \dfrac{{0 \cdot 4}}{{\left( {10 - 0 \cdot 0004} \right)}}$
$ \Rightarrow {R_{sh}} = \dfrac{{0 \cdot 4}}{{9 \cdot 9996}}$
$ \Rightarrow {R_{sh}} = 0 \cdot 04\Omega $.
The shunt resistance is equal to${R_{sh}} = 0 \cdot 04\Omega $.
The correct answer for this problem is option B.

Note: The shunt resistance is used in order to get the measure of the current it may be direct or alternating and it is done by measuring the voltage drop across the resistance whereas moving coil ammeter can be used to measure the current, voltage or resistance if connected them is different ways.