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Sandbox Physics
How physics instruments measure

Inside the instrument

Why a capacitor can behave like an inductor

The same capacitor can behave like an inductor at high frequency. Charge stored on its electrodes holds electric-field energy. Current in its leads and internal connections also holds magnetic-field energy. Changing the frequency changes the balance between these effects. An impedance analyzer measures the response of the complete component.

Sandbox Physics ·

Current size tells only part of the story

Connect a capacitor to an alternating voltage. The source repeatedly charges and discharges its electrodes, which are separated by an insulating material. Charge builds up and retreats on each side. When the voltage reaches a peak, its rate of change briefly becomes zero, so the charging current passes through zero. Near a voltage zero crossing, charging is fastest. The current peak arrives before the voltage peak.

The separation between those peaks, expressed as a fraction of a cycle or an angle, is called a phase difference. An ideal resistor has voltage and current rising together. An ideal capacitor has current leading voltage by a quarter cycle. The size of voltage divided by current loses that distinction. Impedance includes both size and phase, so it describes more of the electrical response.

An analyzer applies a small alternating signal at a known frequency and measures voltage and current against the same timing reference. It can then compare their sizes and the timing of their peaks. Repeat the measurement at another frequency and the instrument reveals how the component responds to faster or slower charging.

Sources: [1][2]

The magnetic effect in the leads grows

A real capacitor includes conducting electrodes, internal connections and leads. Their resistance turns some electrical energy into heat. Current also creates a magnetic field around them. Changing that field produces a voltage that opposes changes in current. The resulting inductance belongs to the component itself; it is often called parasitic inductance.

At a relatively low frequency, increasing the frequency lets a capacitor move more charge back and forth per second at the same voltage. Its capacitive opposition decreases. The inductive opposition grows as the current changes more rapidly. At one frequency these effects cancel, leaving an impedance dominated by loss resistance. This is self resonance. Above it, the current peaks lag the voltage peaks and the component behaves inductively.

Consider a teaching example: a one-microfarad capacitor with 100 nanohenries of internal inductance and 0.1 ohm of series loss resistance. At 100,000 cycles per second its response is still strongly capacitive. Near 503,000 hertz the electric and magnetic storage effects cancel. At two million cycles per second its response is inductive. A frequency change has carried the same component across the dividing line.

f0=12πLCf_0=\frac{1}{2\pi\sqrt{LC}}
The left side is the self-resonant frequency in hertz. On the right, inductance is measured in henries and capacitance in farads. This expression uses a series resistance–inductance–capacitance approximation; the resistance sets the remaining loss at resonance.

Sources: [1][2]

Measure the fixture before interpreting the component

The measurement leads add resistance and inductance too. The two sides of a fixture can also couple capacitively. When an instrument senses voltage and current at its own terminals, this path contributes to the result. Remove the component and measure the open fixture, then join its contacts with a short metal link. The open helps characterize leakage and capacitance across the contacts. The short helps characterize the opposition in series with the path.

A load with a known impedance provides another reference. It helps determine relative scale and timing errors between the voltage and current channels, which open/short correction can handle only under additional assumptions. The standards and the component must share the same contacts. Move the leads and the fixture has changed, so the standards must be measured again. A further known component, kept out of the calibration calculation, can check whether the correction measures another object correctly.

After correction, the capacitor’s own loss and lead inductance should remain. They are properties a circuit will encounter when it uses that component. Removing them as well would erase the high-frequency behaviour the measurement is meant to reveal.

One frequency still cannot uniquely determine the internal circuit. A series resistor and capacitor can be converted into a parallel combination with the same response at that frequency. The converted values change with frequency. Sweeping a range and asking which circuit describes the whole curve makes the result more useful: the model can then predict behaviour across that measured range.

Sources: [1][3][4]

Sources and further reading

  1. Zurich Instruments MFIA User Manual · Signal Processing Basics

    Impedance Measurement, Ideal / Real / Measured, Test Fixtures and Compensation explain complex voltage/current measurement, real component properties and the limits of open/short compensation. The online page was consulted on 28 October 2026.

  2. OpenStax University Physics Volume 2 · §15.3 RLC Series Circuits with AC

    Equations 15.9–15.11 and Figures 15.11–15.13 relate resistance, inductive and capacitive response to current amplitude and phase in a series circuit.

  3. Zurich Instruments MFIA User Manual · Compensation Tutorial

    Configure the Compensation and Carry out the Compensation show why lead geometry must stay fixed and how a known load helps characterize the measurement path.

  4. Keysight E5061B Help · Open/Short/Load Compensation

    Overview, Define Compensation Kit and the standard-acquisition steps describe fixture compensation with declared open, short and load models.

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