This question was previously asked in

LMRC SCTO (Electronics) 2018 Official Paper

Option 3 : 2.24 Ω

CT 1: Current Affairs (Government Policies and Schemes)

54676

10 Questions
10 Marks
10 Mins

__Concept:__

We can extend the range of the 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) = 2 mA

Meter resistance (Rm) = 110 Ω

Required full scale reading (I) = 100 mA

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

\({R_{sh}} = \frac{{110}}{{\left( {\frac{{100}}{{2}} - 1} \right)}} = \frac{110}{49}\;{\rm{Ω }}\)

**R _{sh} = 2.24 Ω**

Hence **option (3)** is the correct answer.

__Important Points__

To increase the ranges of ammeters, 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.