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A galvanometer has a resistance of 60 Ω and gives a full-scale deflection for
a current of 0.15 A. To enhance its measurement range, a shunt resistor is
connected in parallel with the galvanometer.

Calculate the resistance of the shunt resistor required to enable the gal-
vanometer to measure currents up to 1.2 A while maintaining the full-scale

deflection.

Option: 1

0.05 \Omega


Option: 2

0.06 \Omega


Option: 3

0.07 \Omega


Option: 4

0.08 \Omega


Answers (1)

best_answer

To extend the measurement range of a galvanometer and enable it to measure
higher currents, a shunt resistor is connected in parallel with it. The shunt
resistor diverts a portion of the current away from the galvanometer, preventing
it from getting overloaded.
The shunt resistor (R_S) and the galvanometer (G) are connected in parallel,
and the total current (I) is divided between them.
The ratio of the current through the galvanometer to the current through
the shunt resistor is determined by their resistances:

\frac{I_G}{I_S}=\frac{R_S}{R_G}

Given:
Resistance of the galvanometer \left(R_G\right)=60 \Omega Full-scale deflection current
through the galvanometer (I_G) = 0.15 A Maximum current to be measured
\left(I_{\max }\right)=1.2 \mathrm{~A}

The maximum current that can flow through the galvanometer without caus-
ing damage is I_G. To enable the galvanometer to measure currents up to I_{\max },

the current through the galvanometer must not exceed I_G.
Using the ratio equation:

\frac{I_G}{I_S}=\frac{R_S}{R_G}

Substitute the given values:

\frac{0.15 \mathrm{~A}}{1.2 \mathrm{~A}-0.15 \mathrm{~A}}=\frac{R_S}{60 \Omega}

Solving for R_S

R_S=\frac{0.15 \mathrm{~A}}{1.05 \mathrm{~A}} \times 60 \Omega \approx 0.0857 \Omega

Among the answer choices, the closest value is 0.08 \Omega (D). This shunt resistor
value enables the galvanometer to safely measure currents up to 1.2 A while
maintaining the full-scale deflection.
Therefore, the correct answer is:
D) 0.08 \Omega

Posted by

Ajit Kumar Dubey

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