---
title: "High voltage measurement by electrostatic voltmeter"
subject: "High Voltage Engineering"
chapter: 7
key: "semester_8/high_voltage_engineering:electrostatic-voltmeter"
source: https://www.bctengineer.com/q/semester_8/high_voltage_engineering/electrostatic-voltmeter
site: BCT Engineering
---

# High voltage measurement by electrostatic voltmeter

High Voltage Engineering · Chapter 7: Introduction to High Voltage Testing

- Asked in: 2080 Chaitra, 8 marks; 2073 Bhadra, 5 marks (asked 2 times)
- Video: [ELECTROSTATIC VOLTMETER_CONSTRUCTION & WORKING](https://www.youtube.com/watch?v=DozBX3mn9v0) — Simplified EEE Studies
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/high_voltage_engineering/electrostatic-voltmeter
- Whole chapter: https://www.bctengineer.com/md/semester_8/high_voltage_engineering/chapter-7

## Question

Write about the high voltage measurement using electrostatic voltmeter. Explain the working principle of electrostatic voltmeter with neat diagrams.

## Short answer

An electrostatic voltmeter measures voltage by the attractive force between plates: F ∝ V², reading true rms. In the attracted-disc type, a movable disc inside a guard ring is pulled toward the HV electrode; deflection via spring and mirror scale gives voltage. It draws negligible current and works up to about 1 MHz.

## Answer

An **electrostatic voltmeter** measures voltage from the attractive force between two charged electrodes. Since the force depends on $V^2$, it reads the **true rms value** of AC (of any waveform) and the value of DC, and it draws almost no current.

#### Principle

For two parallel plates of area $A$ separated by $x$, the stored energy is $W = \frac12 CV^2$ with $C = \varepsilon_0 A/x$. The force between the plates is

$$
\begin{aligned}
F &= \frac{dW}{dx} = \frac12 V^2\frac{dC}{dx} \\
&= -\frac12\,\frac{\varepsilon_0 A V^2}{x^2}\quad(\text{attraction})
\end{aligned}
$$

For AC, $V = V_m\sin\omega t$, and the moving system responds to the average force:

$$
F_{av} = \frac{\varepsilon_0 A}{2x^2}\cdot\frac1T\int_0^T v^2\,dt = \frac{\varepsilon_0 A}{2x^2}V_{rms}^2
$$

So the deflection measures $V_{rms}$.

#### Construction (attracted-disc type)

```text
          HV electrode  (V)
   ===============================
                 |  gap x
   ======  [ movable disc ]  =====
   guard     |  (earthed)    guard
   ring      |               ring
             +-- spring / balance
             +-- mirror -> lamp & scale
                 |
               earth
```

- **High-voltage electrode:** a large plane disc (or sphere) connected to the voltage to be measured.
- **Low-voltage electrode:** an earthed plane with a **guard ring**; a small movable disc sits in a hole at its centre, flush with the plane.
- The **guard ring** keeps the field over the movable disc uniform, so the simple parallel-plate formula holds and edge effects are removed.
- The movable disc is held by a spring or a balance beam. Its small movement is magnified by a mirror and light beam on a scale, or the force is balanced by weights or a restoring spring (absolute instruments such as the Kelvin attracted-disc electrometer).
- The whole system may be enclosed in compressed gas (N₂, SF₆) or vacuum to raise the range.

#### Working

1. Voltage is applied between the HV electrode and the earthed plane.
2. The movable disc is attracted towards the HV electrode with force proportional to $V^2$.
3. The disc moves until the spring force balances the electrostatic force; the deflection is read on the scale, calibrated directly in kV.
4. For range change, the gap $x$ is adjusted (larger gap for higher voltage).

#### Features

| Advantages | Limitations |
|---|---|
| Reads true rms of any waveform | Force is small; needs careful calibration |
| Very small loading (a few pF) | Not suitable for impulse voltages |
| Works on DC and AC up to about 1 MHz | Affected by dust, external fields |
| Accuracy about ±0.1% to ±1% | Bulky for very high voltages |
| No power drawn after charging | Square-law scale (cramped at low end) |

Ranges of about 600 kV in air and up to about 1000 kV with compressed gas insulation are achieved.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. On what does the electrostatic voltmeter's deflection depend?
   A. Force between charged electrodes, proportional to V^2
   B. Current through the meter, proportional to V
   C. Magnetic field, proportional to V
   D. Heat produced, proportional to V
   Answer: A. F = 1/2 V^2 dC/dx, an attraction force proportional to V squared. (Key point: Principle)

2. Why does it read the rms value of AC?
   A. It averages V over a cycle, and the average force is proportional to V_rms^2
   B. It reads the peak value only
   C. It rectifies the voltage first
   D. It uses the mean of V, which is zero
   Answer: A. The moving system responds to the average force, proportional to the average of v^2, which is V_rms^2. (Key point: True rms reading)

3. What is the function of the guard ring?
   A. To carry the leakage current to the meter
   B. To keep the field over the movable disc uniform and remove edge effects
   C. To increase the force by increasing the gap
   D. To shield the meter from magnetic fields
   Answer: B. A uniform field makes the parallel-plate formula valid. (Key point: Guard ring)

4. Which is a limitation of the electrostatic voltmeter?
   A. It cannot measure DC
   B. It draws a large current
   C. It is not suitable for impulse voltages and has a square-law scale
   D. It reads only the peak
   Answer: C. It works for DC and AC with very small loading, but not for impulses, and the scale is cramped at the low end. (Key point: Limitations)

## Related in High Voltage Engineering

- [HV AC measurement methods and electrostatic voltmeter](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Ahv-ac-measurement-electrostatic-voltmeter) — High Voltage Engineering, chapter 7, asked 2×
- [General HV tests and electrostatic voltmeter](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Ageneral-tests-electrostatic-voltmeter) — High Voltage Engineering, chapter 7
- [Series impedance voltmeter and its drawbacks](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Aseries-impedance-voltmeter) — High Voltage Engineering, chapter 7

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