Question

The resistance of a galvanometer is 50 ohm and the maximum current which can be passed through it is 0.002 A. What resistance must be connected to it in order to convert it into an ammeter of range 0 – 0.5 A?

A. 0.2 ohm
B. 0.002 ohm
C. 0.02 ohm
D. 0.5 ohm

Answer 1

Hint: As the question is to convert a galvanometer to an ammeter of the range 0 – 0.5 A, so, we are supposed to find the value of the shunt resistance of this galvanometer. This is a direct question. The formula that relates the current range of the ammeter, the maximum current of the galvanometer, the resistance of the galvanometer and the shunt resistance is as follows can be used to find the value of the shunt resistance.
Formula used:
\[\dfrac{i}{{{i}_{G}}}=1+\dfrac{G}{S}\]

Complete answer:
From the question, we have the data as follows.
The initial resistance of the galvanometer is equal to 50 ohms.
\[\Rightarrow G=50\Omega \]
The maximum value of the current that can be passed through a galvanometer is 0.002 A.
\[\Rightarrow {{i}_{G}}=0.002A\]
The range of the reading of the current that this ammeter should show is 0 – 0.5 A.
\[\begin{align}
  & i=0.5-0 \\
 & \Rightarrow i=0.5A \\
\end{align}\]
The formula that relates the current range of the ammeter, the maximum current of the galvanometer, the resistance of the galvanometer and the shunt resistance is as follows.
\[\dfrac{i}{{{i}_{G}}}=1+\dfrac{G}{S}\]
Where i is the maximum current representation in ammeter, G is the galvanometer resistance, S is the shunt resistance and \[{{i}_{G}}\]is the galvanometer current.
Substitute the given values in the above equation.
\[\dfrac{0.5}{0.002}=1+\dfrac{50}{S}\]
Continue the further calculation to find the value of the shunt resistance.
\[\begin{align}
  & 250-1=\dfrac{50}{S} \\
 & \Rightarrow 249=\dfrac{50}{S} \\
 & \Rightarrow S=0.2\,\Omega \\
\end{align}\]
As, the value of the shunt resistance obtained is equal to 0.2 ohms.

So, the correct answer is “Option A”.

Note:
The question statement is a bit twisted, instead of directly asking for the shunt resistance, the value of the resistance that must be connected to it in order to convert the galvanometer into an ammeter is being asked. The units of the parameters should be taken care of.