Concept:

The shunts and multipliers are used in the extension of the range of voltmeters and ammeters.

For ammeter, a low shunt resistance (Rsh ≪≪ Rm) is connected to increase its range

\({{\bf{R}}_{{\bf{sh}}}} = \frac{{{{\bf{R}}_{\bf{m}}}}}{{{\bf{m}} - 1}}\)

Rsh = shunt resistance

Rm = meter resistance

m = I / I_m = multiplying factor or multiplying power

For the voltmeter, a high series resistance (Rse ≫≫Rm) is connected to increase its range

\({{\bf{R}}_{{\bf{se}}}} = {{\bf{R}}_{\bf{m}}}\left( {{\bf{m}} - 1} \right)\)

\({\rm{m}} = \frac{{\rm{V}}}{{{{\rm{V}}_{\rm{m}}}}}\) = multiplying power/factor

Calculation:

Given meter resistance

R_mx = 1.2 Ω, R_my = 1.5 Ω 

Shunt resistances need to be connected to increase the range of the meters to 15 A

I_mx = 150 mA, I_my = 250 mA

\(\begin{array}{l} {R_{shx}} = \frac{{1.2}}{{\left( {\frac{{15}}{{150 \times {{10}^{ - 3}}}} - 1} \right)}} = 0.0121\;{\rm{Ω }}\\ {R_{shy}} = \frac{{1.5}}{{\left( {\frac{{15}}{{250 \times {{10}^{ - 3}}}} - 1} \right)}} = 0.02542\;{\rm{Ω }} \end{array}\)

Equivalent resistance offered by meter x

R_x = R_mx || R_shx = 0.012 Ω 

Equivalent resistance offered by meter y

R_y = R_my || R_shy = 0.025 Ω 

Current through ammeter ‘x’ is

\(I = \left( {\frac{{0.025\times15}}{{0.012 + 0.025}}} \right) = 10.13\; A\)