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

Given Data:

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

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

R_s = (I_g · R_g) / (I - I_g)

Substituting the given values:

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

Convert currents to amperes:

R_s = (0.0001 · 50) / (0.01 - 0.0001)

Numerator:

0.0001 × 50 = 0.005

Denominator:

0.01 - 0.0001 = 0.0099

Calculate:

R_s = 0.005 / 0.0099 ≈ 0.505Ω

Final Answer:

The shunt resistance required is approximately:

R_s = 0.5Ω

This resistance (R_s) 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.