How is a shunt used to convert a galvanometer into an ammeter?

Shunt and Its application

To convert a galvanometer into an ammeter, very low resistance is connected in parallel with a galvanometer coil so that maximum current can flow through it which is called the shunt. Shunt provides an alternative path for excess current. It is used to convert galvanometers into ammeters.

Conversion of galvanometer into ammeter:

Let, S be the value of shunt resistance and G be the galvanometer resistance, I be the total current through the circuit. Since resistance G and S are parallel, the effective resistance R of the circuit is

\(\frac1R=\frac1G+\frac1S\)

\(\Rightarrow R=\frac{GS}{G+S}\), Since S is small, R is very small.

But potential across G = potential across S.

\(V=\frac{GS}{G+S}\times I\)

Current through G is 

\(I_g=\frac VG=\frac{GS}{G\left(G+S\right)}\times I=\frac S{G+S}\times I\)

And current through S is

\(I_S=\frac VS=\frac{GS}{S\left(G+S\right)}\times I=\frac G{G+S}\times I\)

Since the resistance of shunt is small, the fraction of current through the galvanometer, \(\left(\frac S{G+S}\right)I\) is small.

Again, the current through the shunt = I - I_g

Since potential difference across Shunt (S) = potential difference across G

Or, \(\left(I-I_g\right)S=I_gG\)

\(\Leftarrow S=\frac{I_g}{I-I_g}G\)

This is the required value of shunt which when connected in parallel with the coil to convert the galvanometer into an ammeter of the required range.