Measurement of Capacitance - GATE Notes & Videos for Electrical Engineering - Electrical

Measurement of Capacitance with a Digital Multimeter

To measure the capacitance of a capacitor accurately one normally uses an LCR meter (measures inductance L, capacitance C and resistance R) because it can measure at specified test frequencies and give precise values including ESR (equivalent series resistance). A digital multimeter (DMM) with a capacitance function can also measure capacitance and is useful for quick checks, but its range and accuracy are limited compared with an LCR meter.

Capacitance - definition and units

• Capacitance is the ability of a device (capacitor) to store electric charge. For a capacitor with charge Q and voltage V, capacitance C is C = Q / V.
• The SI unit of capacitance is the farad (F). One farad equals one coulomb per volt. Because one farad is large for most practical components, common units are microfarad (μF), nanofarad (nF) and picofarad (pF).
• A capacitor consists of two conducting plates separated by a dielectric. Its capacitance depends on plate area, separation and the dielectric constant.

Working principle of capacitance measurement by a DMM

A typical DMM measures capacitance by applying a known test current to the capacitor and measuring the resulting rate of voltage change. The relation between current and voltage for a capacitor is

I = C · dV/dt

Thus, with a known test current I and a measured dV/dt, the meter computes capacitance C = I / (dV/dt). In practice the meter charges the capacitor with an internal current source and times the voltage rise; for small capacitances the voltage rises quickly, for large capacitances it rises slowly.

Important practical notes:

• Measurement by the DMM is frequency-dependent and the DMM effectively measures capacitance at its internal test conditions; an LCR meter measures at selectable frequencies (for example 1 kHz, 100 Hz) and is more suitable when frequency dependence matters.
• The meter reading can be affected by ESR and by other components connected to the capacitor when it remains in circuit; for accurate results the capacitor should normally be disconnected from the circuit.

Precautions before measuring

• Always disconnect power from the circuit before removing or measuring a capacitor.
• Capacitors can retain charge. Discharge the capacitor safely by connecting a resistor across its terminals. Do not short the terminals directly with a screwdriver or wire.
• Use an appropriate resistor to discharge: for example a resistor of a few kiloohms to tens of kiloohms rated for sufficient power (a 5 W resistor is commonly recommended for larger capacitors).
• Observe polarity for electrolytic (polarised) capacitors. Incorrect polarity can damage the capacitor or cause an explosion.
• Visually inspect the capacitor for bulging, leakage, cracks or other signs of failure. Do not attempt to measure or charge a visibly damaged capacitor.
• Do not touch the metal tips of the test leads during measurement; the capacitance of the leads and stray capacitances can introduce error, especially for small capacitors.

Measuring capacitance - general guidance

Capacitance can be measured by a DMM that has a capacitance function, typically marked "F" or a capacitor symbol. If precision is required, use an LCR meter. The following procedures describe two practical methods suitable for laboratory or workshop use.

Method 1: Using a digital multimeter with a capacitance range

1. Switch off and isolate the circuit; verify the circuit is de-energised by confirming zero volts across the relevant points with the meter set to voltage mode.
2. Visually inspect the capacitor for damage (bulge, leak or cracks). Replace if faulty.
3. Safely discharge the capacitor by connecting a suitable resistor across the terminals. Wait until the voltage is essentially zero.
4. If possible, remove the capacitor from the circuit; in-circuit measurement often gives incorrect results due to parallel or series components. If removal is not possible, be aware the reading may be unreliable unless using an LCR meter designed for in-circuit measurement.

5. Turn the meter dial to the capacitance position (marked "-|(-", "F" or similar). If the capacitance function is a secondary function, use the shift or function key as required.

6. If the meter is not auto-ranging, select an approximate range for the expected capacitance.
7. Insert the black probe into the COM socket and the red probe into the socket labelled for capacitance measurement (often marked with the capacitor symbol).

8. Some meters provide dedicated capacitance sockets (for example small clips or ports where the capacitor can be placed directly). If present, use them for convenience and better repeatability.

9. Press the REL (relative) or zero function if available to subtract the capacitance of the test leads and hold a zero reference; this is useful when measuring very small capacitances.
10. Connect the test leads to the capacitor terminals (black to negative, red to positive for polarised capacitors). For non-polar capacitors the polarity does not matter.

11. The meter will charge the capacitor and indicate the measured value. Wait until the displayed value stabilises.
12. If the meter displays "OL" or displays a reading that does not stabilise, increase the range. If the reading remains out of range the capacitor value is beyond the meter's capability or the capacitor may be faulty.
13. When finished, remove the red probe first, then the black probe.
14. Turn off the meter or switch it back to a different function to preserve battery life.

Notes and tips for Method 1

• Use the REL or zero function to eliminate test lead capacitance when measuring small capacitors.
• If a capacitor is suspected to have high ESR or leakage, the DMM capacitance function may give incorrect values; specialised equipment (LCR meter or capacitance bridge) should be used.
• Do not short capacitor terminals to discharge them; use a resistor as described in the precautions.
• Analogue multimeters typically cannot measure capacitance directly because they lack a test current source and timing circuitry; they can, however, be used for basic go/no-go checks (charging behaviour, leakage) in simple tests.

Method 2: Time-constant (RC) method - simple practical test using a battery, resistor and stopwatch

This method measures the charging time to a known fraction of the supply voltage. When a capacitor charges through a resistor from a step voltage, the voltage across the capacitor v(t) follows

v(t) = V_s · (1 - e^(-t/RC))

At time t = RC (the time constant τ), the capacitor voltage reaches approximately 63.2% of the final value V_s. By measuring the time taken to reach 63.2% of V_s, one can compute C = τ / R.

The procedure is:

1. Disconnect and fully discharge the capacitor.
2. Choose a resistor R of known value (for example 10 kΩ). Ensure the resistor can safely dissipate the expected power.
3. Connect the resistor in series between the battery positive and the capacitor positive terminal; connect the battery negative to the capacitor negative terminal.
4. Use a multimeter to monitor the capacitor voltage and start a stopwatch as you connect the battery to begin charging.
5. Stop the stopwatch when the multimeter reads 63.2% of the battery voltage (for example, 0.632 × V_s). Record the time t (this is approximately τ = RC).
6. Compute capacitance using C = t / R.

Worked example (from the reference data)

Given: a capacitor rated 16 V, 470 μF; supply used is 9 V; resistor R = 10 kΩ; measured time t to reach 63.2% of 9 V (≈ 5.7 V) was 4.7 s. Compute C.

Sol.

τ = RC

C = τ / R

Substitute τ = 4.7 s and R = 10 000 Ω.

C = 4.7 s / 10000 Ω

C = 0.00047 F

C = 470 μF

C = 0.47 mF

Thus the measured capacitance is 470 μF, which matches the rated 470 μF.

Common measurement errors and troubleshooting

• Measuring the capacitor while it is still connected in circuit may give an incorrect high or low reading due to parallel resistances or series inductances; where possible, remove the capacitor before measurement.
• Residual charge on the capacitor will cause erroneous readings; always discharge first.
• Test lead capacitance and stray capacitance can affect readings for small capacitors; use REL/zero function or short the leads and null the meter reading before testing.
• Extreme temperature, electrolyte leakage and ageing change capacitor value; compare measured value with the nominal tolerance indicated on the component.
• A reading that is very low or zero may indicate an open capacitor; a reading of zero or a very small resistance during a simple resistance test may indicate a shorted capacitor.
• Very high ESR or internal leakage can make a capacitor appear to have lower capacitance on a simple DMM measurement; specialised ESR meters or an LCR meter should be used for detailed diagnostics.

Important practical points (summary)

• Do not touch the tips of test leads during measurement; this adds stray capacitance and error.
• Some DMMs include dedicated capacitor sockets - use them for small components to improve repeatability.
• Always discharge capacitors with a resistor; never short them directly.
• Observe polarity for electrolytic capacitors; reverse polarity can damage or explode the capacitor.
• An analogue multimeter cannot accurately measure capacitance but can perform simple functional checks.
• Use REL mode for very small capacitance readings to cancel lead capacitance.
• For precise capacitance measurement or for in-circuit measurement, use an LCR meter.
• Replace capacitors that show bulges, cracks, leaks or values outside the specified tolerance range.

Importance of capacitance measurement in electrical systems

• Capacitors age and their capacitance typically decreases and ESR increases with use; measurement assesses component health.
• Detecting faulty capacitors prevents system malfunction, reduced performance or catastrophic failure (for example, explosion of an electrolytic capacitor).
• A faulty capacitor can cause loss of filtering, unstable supply rails, motor start failures (capacitor-start motors), and malfunction in power factor correction units.
• Shorted capacitors can blow fuses or damage other components; open capacitors can interrupt circuits where capacitance is required for timing or coupling.
• Regular testing of capacitors in power supplies, motor drives, and power factor correction panels is part of preventive maintenance.

Further reading and tools

• Use an LCR meter for precision measurements, frequency-dependent data and ESR measurement.
• Refer to component datasheets for rated capacitance, tolerance, voltage rating and recommended test conditions.
• For reliability testing, environmental effects (temperature, ripple current) and lifetime need to be considered following manufacturer recommendations.

Optional concise summary

Digital multimeters can give useful approximate capacitance measurements using an internal test current and timing; however, for accurate, frequency-dependent or in-circuit measurements an LCR meter or appropriate specialised tester is recommended. Always isolate and safely discharge capacitors before measuring, observe polarity, and be aware of the limitations of the meter and effects of ESR, lead capacitance and connected circuitry.