Question

A moving-coil milliammeter has a resistance of 5 Ω and a full-scale deflection of 20 mA. Determine the resistance of a shunt to be used so that the instrument could measure currents upto 500 mA at 20° C. What is the percentage error in the instrument operating at a temperature of 40°C ? Temperature co-efficient of copper = 0.0039 per °C.

Answer 1

The resistance of a shunt to be used is 120 Ω.

The percentage error in the instrument operating at a temperature of 40°C is 7.8%.

How to calculate the resistance?

The resistance of a shunt to be used is calculated as follows.

`I_f = I_ m (1 + (R_s)/(R_m) )`

where;

• If is the full-scale current (500 mA),
• Im is the full-scale deflection current of the meter (20 mA),
• Rs is the shunt resistance = ?
• Rm is the meter resistance (5 Ω)

500 mA = 20 mA (1 + Rs/5)

500 mA/20 mA = (1 + Rs/5)

25 = 1 + Rs/5

Rs/5 = 25 - 1

Rs/5 = 24

Rs = 5 x 24

Rs = 120 Ω

The change in the resistance of the copper is calculated as;

ΔR = Rm × α × ΔT

ΔR = 5Ω × 0.0039 / °C × (40⁰C - 20⁰C)

ΔR = 0.39 Ω

Percentage error = (0.39Ω / 5Ω) x 100%

Percentage error = 7.8%