This question was previously asked in

ESE Electrical 2016 Paper 1: Official Paper

Option 1 : with shunt resistance of 0.0001 Ω

CT 3: Building Materials

2894

10 Questions
20 Marks
12 Mins

Concept:

We can extend the range of ammeter by keeping a shunt resistance.

Here Rm = internal resistance of the coil

Rsh = Shunt resistance

I = Required full-scale range

Im = Full scale deflection of current

As the two resistances, Rm and Rsh are in parallel, the voltage drop across the resistance is equal.

\({I_m}{R_m} = \left( {I - {I_m}} \right){R_{sh}}\)

\({R_m} = \left( {\frac{I}{{{I_m}}} - 1} \right){R_{sh}}\)

\(\Rightarrow {R_{sh}} = \frac{{{R_m}}}{{\left( {\frac{I}{{{I_m}}} - 1} \right)}}\)

\(\Rightarrow {R_{sh}} = \frac{{{R_m}}}{{\left( {m - 1} \right)}}\)

Where \(m = \frac{I}{{{I_m}}}\)

‘m’ is called multiplying power

Calculation:

Given that,

Full scale deflection current (Im) = 10 mA

Full-scale deflection voltage (Vm) = 10 mV

Meter resistance (Rm) = V_{m}/I_{m }= 1 Ω

Required full scale reading (I) = 100 A

\({R_{sh}} = \frac{{{R_m}}}{{\left[ {\frac{I}{{{I_m}}} - 1} \right]}}\)

\({R_{sh}} = \frac{{1}}{{\left( {\frac{{100}}{{0.01}} - 1} \right)}} = 0.0001\;{\rm{\Omega }}\)

Note:

To increase the ranges of ammeter, we need to connect a small shunt resistance in parallel with ammeters.

To increase the ranges of a voltmeter, we need to connect a high series of multiplier resistance in series with voltmeters.