Shunts and Multipliers

1. Shunt:

A shunt is a low resistance usually used to convert a galvanometer to an ammeter. It is usually connected in parallel with the galvanometer.

I – Current to be measured

I_g – Current through the galvanometer

R_s – Resistance of the shunt

R_g – Resistance of galvanometer

Note: The voltage across the shunt is the same as that across galvanometer.

Vg=VsIgRg=(I−Ig)Rg

Example:

A galvanometer gives a full scale deflection when a current of 10mA flows through it. How would  you convert it to an ammeter capable of reading 3Aif the resistance of the galvanometer is 5Ω?

Solution:

To do this, we connect a resistor of low resistance called shunt in parallel with the galvanometer.  The value of such shunt is calculated below:

10mA=101000=0.01A

p.d across galvanometer = p.d across shunt

Igrg=IsRsRs=IgrgIs=0.01×52.99=0.0167Ω

Thus, a shunt of 0.0167Ω is needed.

2. Multiplier:

A multiplier is a high resistance usually used to convert a galvanometer to a voltmeter. It is usually connected in series with the galvanometer.

Example:

To convert a galvanometer to a voltmeter ,we need a multiplier Rso that the galvanometer could  read 20V at full scale deflection of 10mA. Find the value of R if the internal resistance of the  galvanometer is 6Ω. Solution:

r=6Ω20v=V1+V2∴20=0.01r+0.0RR=1994Ω