JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III MEASUREMENTS AND INSTRUMENTATION Previous Question Paper (March - 2021 - R18)

To convert a d'Arsonval movement into a multi-range voltmeter using a potential divider arrangement, we calculate the series multiplier resistances (R1, R2, R3, R4) for each range. The total resistance R_T for a range V is given by R_T = V / I_m, where I_m = 1mA = 0.001A. The internal resistance R_m = 100 Ω.

For the 10V range: R_T1 = 10 / 0.001 = 10,000 Ω. R1 = R_T1 - R_m = 10,000 - 100 = 9,900 Ω.

For the 50V range: R_T2 = 50 / 0.001 = 50,000 Ω. R2 = R_T2 - R_T1 = 50,000 - 10,000 = 40,000 Ω.

For the 250V range: R_T3 = 250 / 0.001 = 250,000 Ω. R3 = R_T3 - R_T2 = 250,000 - 50,000 = 200,000 Ω.

For the 500V range: R_T4 = 500 / 0.001 = 500,000 Ω. R4 = R_T4 - R_T3 = 500,000 - 250,000 = 250,000 Ω.

The required series resistances are 9.9 kΩ, 40 kΩ, 200 kΩ, and 250 kΩ respectively.

Electrostatic voltmeters operate on the principle of electrostatic attraction between two plates. Their range is typically limited by the mechanical construction and the dielectric strength of the air gap. To extend the range, two primary methods are used:

• Capacitive Potential Divider: This is the most common method for AC measurements. A high-voltage capacitor is connected in series with the electrostatic voltmeter. The total voltage is divided between the series capacitor and the internal capacitance of the meter. The voltage across the meter is V_m = V * (C_s / (C_s + C_m)), where C_s is the series capacitor and C_m is the meter capacitance.
• External Potential Divider (Resistive): For DC measurements, a high-resistance potential divider (potentiometer) is used to drop the voltage to a level within the meter's rating. However, this draws current and reduces the high input impedance advantage of the electrostatic voltmeter.
• Compressed Gas Insulation: By enclosing the movement in a container filled with an inert gas like Nitrogen or Sulfur Hexafluoride (SF6) at high pressure, the dielectric strength of the insulation is significantly increased, allowing the meter to withstand higher voltages without arcing.