Question

A millimeter reading from 0 to 50 mA has a resistance of 396 ohm. How will you change it so that it can be used as an ammeter to measure a maximum current of 5A?

Answer 1

Hint: A galvanometer can be used as an ammeter by connecting a very small shunt resistance in parallel with the galvanometer. This causes an increase in the current range of the whole setup as a lot of current passes through the shunt resistance. Find the potential difference across the multimeter and the shunt resistance. Equate these two equations for potential difference and then obtain an expression for shunt resistance. Substitute the values in the formula and find the value of shunt resistance.
Formula used:
${I}_{g}G=\left(I-{I}_{g}\right)S$

Complete answer:

Let the resistance of Galvanometer be G and current flowing through it be ${I}_{g}$.
     The shunt resistance be S.
Then, the current flowing through the shunt resistance is $I-{I}_{g}$.
Given: ${I}_{g}$= 50 mA=0.05 A
            G= 396 ohm
            I= 5A
From the above figure, potential difference across galvanometer is given by,
${V}_{g}= {I}_{g}G$
Similarly, potential difference across the shunt resistance is given by,
${V}_{s}=\left(I-{I}_{g}\right)S$
We know the potential difference across the galvanometer is the same as the potential difference across shunt resistance.
$\therefore {V}_{g}={V}_{s}$
Substituting values in above equation we get,
${I}_{g}G=\left(I-{I}_{g}\right)S$
$\Rightarrow S= \dfrac {{I}_{g}G}{I-{I}_{g}}$
Substituting values in above equation we get,
$S= \dfrac {0.05 \times 396}{5-0.05}$
$\Rightarrow S= \dfrac {19.8}{4.95}$
$\Rightarrow S=4 \Omega$
Hence, a galvanometer of resistance $396 \Omega$ and current of 50mA can be converted into an ammeter to read a maximum current of 5A by connecting a shunt resistor of $4\Omega$.

Note:
Students must remember how to convert a galvanometer into an ammeter or a voltmeter. To convert a galvanometer into an ammeter, a very small shunt resistance has to be connected in parallel always. While to convert a galvanometer into a voltmeter, a large resistance has to be connected in series. The galvanometer resistance is considered as a simple resistance which is in series with an ideal galvanometer. An ideal galvanometer has zero resistance.