Shunt Resistance Formula

Answer: B. 200 Ω

A shunt resistance of 50 Ohms is required to extend an ammeter’s range from 100 μA to 500 μA. The value of the internal resistance of the ammeter is 200 Ohm.

Solution:

Shunt resistances are used to extend the range of basic ammeters. A basic DC ammeter is a PMMC d’Arsonval galvanometer; the basic ammeter coil is small in size and lighter in weight, so it can only carry a very small amount of current. If we want to construct a basic ammeter to carry large currents greater than 100 mA, coil winding must be very large, and it will become heavy, so the meter will become bulky, which will be impractical.

To measure large currents, we connect a shunt; the shunt is a low resistance connected in parallel with a basic meter, as the value of shunt resistance is a small majority of current will bypass through the shunt, and a very small of current will pass through the meter coil. The connection between the shunt and the basic meter is shown below.

Where R_Sh= shunt resistance,

R_m= meter resistance,

I_m= full-scale deflection current of meter,

And the value shunt resistance is given as R_Sh=R_m/(m-1),

Here, m = multiplying power =I/I_m

I= required current to be measured

Given,

I=500 μA 

I_m=100 μA

R_sh=50  

We know, R_Sh=R_m/(m-1)

R_m=R_sh.(m-1)

Here m=I/I_m=500/100=5

Then

R_m=50.(5-1)=200 Ohms

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