JNTU B.Tech III MEASUREMENTS AND INSTRUMENTATION Previous Question Paper (September - 2021 - R18)

The attracted disc electrostatic voltmeter operates on the principle of electrostatic attraction between two charged electrodes. It consists of a fixed plate and a movable disc (the attracted disc) suspended by a spring. When a potential difference is applied across the plates, an electrostatic force of attraction is generated, pulling the movable disc towards the fixed plate. This force is proportional to the square of the applied voltage.

The force of attraction F is given by:

where V is the applied voltage and dC/dx is the rate of change of capacitance with respect to the distance between the plates. As the disc moves, the spring provides a restoring force proportional to the displacement. The equilibrium position of the disc indicates the voltage value on a calibrated scale. This instrument is primarily used for high voltage measurements as the force is significant at higher potentials and it draws negligible current, making it ideal for high-impedance circuits.

Given: Full-scale current I_m = 10 mA = 0.01 A, Voltage drop V_m = 100 mV = 0.1 V. The internal resistance of the meter is R_m = V_m / I_m = 0.1 / 0.01 = 10 Ω.

1. Shunt resistance for 100 A: The total current I = 100 A. The shunt resistance R_sh = R_m / (I/I_m - 1) = 10 / (100/0.01 - 1) = 10 / 9999 ≈ 0.0010001 Ω. Power dissipation in shunt P_sh = I_sh² * R_sh = (99.99)² * 0.0010001 ≈ 10 W.
2. Multiplier resistance for 1000 V: The total voltage V = 1000 V. The multiplier resistance R_se = (V/V_m - 1) * R_m = (1000/0.1 - 1) * 10 = 9999 * 10 = 99,990 Ω. Power dissipation in multiplier P_se = I_m² * R_se = (0.01)² * 99990 = 9.999 W.