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Q.

A galvanometer has coil of resistance 50Ω and shows full deflection at 100μA . The resistance to be added for the galvanometer to work as an ammeter of range 10mA is nearly

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a

0.5Ω in series

b

0.5Ω in parallel

c

5.0Ω in series

d

5.0Ω in parallel

answer is B.

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Detailed Solution

Given Data:

  • Resistance of the galvanometer (Rg) = 50Ω
  • Full-scale deflection current (Ig) = 100 μA = 0.1 mA
  • Desired range of the ammeter (I) = 10 mA

The formula for the shunt resistance (Rs) connected in parallel is:

Rs = (Ig · Rg) / (I - Ig)

Substituting the given values:

Rs = (0.1 mA · 50Ω) / (10 mA - 0.1 mA)

Convert currents to amperes:

Rs = (0.0001 · 50) / (0.01 - 0.0001)

Numerator:

0.0001 × 50 = 0.005

Denominator:

0.01 - 0.0001 = 0.0099

Calculate:

Rs = 0.005 / 0.0099 ≈ 0.505Ω

Final Answer:

The shunt resistance required is approximately:

Rs = 0.5Ω

This resistance (Rs) should be connected in parallel with the galvanometer to ensure that most of the 10 mA current bypasses the sensitive galvanometer coil, protecting it from damage.

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A galvanometer has coil of resistance 50Ω and shows full deflection at 100μA . The resistance to be added for the galvanometer to work as an ammeter of range 10mA is nearly