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ESE Electrical 2015 Paper 1: Official Paper

Option 2 : 0.01 Ω

CT 1: Network Theory 1

11532

10 Questions
10 Marks
10 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) = 1 mA

Meter resistance (Rm) = 50 Ω

Required full scale reading (I) = 5 A

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

\({R_{sh}} = \frac{{50}}{{\left( {\frac{{5}}{{1 \times {{10}^{ - 3}}}} - 1} \right)}} \approx 0.01{\rm{\Omega }}\)