Question

If the galvanometer current is $10mA$, resistance of the galvanometer is $40\Omega $ and the shunt of $2\Omega $ is connected to galvanometer, the maximum current which can be measured by this ammeter is:
A. $0.21A$
B. $2.1A$
C. $210A$
D. $21A$

Answer 1

Hint:We know that the shunt is always connected parallel to the resistance in the galvanometer. Here, in this question, the galvanometer current, resistance of the galvanometer and resistance of the shunt is given. We will use the formula for the ammeter current which is the function of all these given values.

Formula used:
${I_A} = \left( {\dfrac{{S + {R_g}}}{S}} \right){I_g}$,
where, ${I_A}$ is the maximum current measured by the ammeter,$S$ is the shunt resistance, ${R_g}$ is the resistance of the galvanometer and ${I_g}$ is the galvanometer current.

Complete step by step answer:
We are given that galvanometer current ${I_g} = 10mA = 0.01A$, resistance of the galvanometer ${R_g} = 40\Omega $ and the resistance of the shunt $S = 2\Omega $.
We know that the ammeter current is given by the formula ${I_A} = \left( {\dfrac{{S + {R_g}}}{S}} \right){I_g}$.
We will now put the given values in this formula.
${I_A} = \left( {\dfrac{{S + {R_g}}}{S}} \right){I_g} \\
\Rightarrow{I_A}= \left( {\dfrac{{2 + 40}}{2}} \right) \times 0.01 \\
\therefore{I_A}= 0.21A$
Thus, our final answer is: If the galvanometer current is $10mA$, resistance of the galvanometer is $40\Omega $ and the shunt of $2\Omega $ is connected to galvanometer, the maximum current which can be measured by this ammeter is $0.21A$.

Hence, option A is the right answer.

Note:We know that the galvanometer is a very sensitive instrument therefore it cannot measure heavy currents. In order to convert a galvanometer into an ammeter, a very low resistance known as shunt resistance is connected in parallel to the galvanometer. The value of shunt is so adjusted that most of the current passes through the shunt. In this way a galvanometer is converted into an ammeter and can measure heavy currents without fully deflected.