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Capacitor AC Characteristics · Voltage-Current Phase Difference

Apply a sinusoidal AC voltage \(v(t) = V_m \sin(2\pi f t)\) to a capacitor and observe the phase relationship between voltage \(u(t)\) and current \(i(t)\)
Capacitor current unit: amperes (A)

Signal Source & Capacitor Parameters

1.00 V
0.2 V5 V
50.0 Hz
10 Hz500 Hz

Frequency affects capacitive reactance, changing current amplitude; phase difference remains at -90°

2000 μF
1000 μF5000 μF

Current leads voltage by \(90^\circ\), amplitude \(I_m = V_m \cdot \omega C\) (A)

Capacitor Phase Difference Theory

Capacitor \(C\) \(\varphi = -90^\circ\) Current leads voltage by \(90^\circ\)
Expression: \(i_C = C\frac{dv}{dt}\)
In sinusoidal steady-state, current leads voltage by \(90^\circ\). Capacitor current unit: A
Current amplitude: \(I_{Cm} = V_m \cdot 2\pi f C\ \text{(A)}\), Capacitive reactance \(X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C}\).

Capacitor · Voltage \(u_C(t)\) and Current \(i_C(t)\) (A)

Phase Diff \(\Delta\varphi = -90^\circ\) (Current Leads)
Capacitive component: current leads voltage by 90°, \(i_C(t)\) peak occurs \(\frac{T}{4}\) before voltage peak (current unit: A)

Waveform Observation Key Points

• Capacitor: current \(i_C\) zero-crossing leads voltage \(u_C\) by \(90^\circ\).
• Current is zero at voltage peak, voltage is zero at current peak.
• Adjusting frequency \(f\) or capacitance \(C\) changes current amplitude, but phase difference remains at \(-90^\circ\).
• Capacitor current unit: A, consistent with inductor current unit.

Effect of Parameters on Amplitude

\(I_{Cm} = V_m \cdot 2\pi f C\ \text{(A)}\)
Increase voltage \(V_m\) → current increases linearly;
Increase frequency \(f\) → current increases;
Increase capacitance \(C\) → current increases;
Capacitive reactance \(X_C = \frac{1}{\omega C}\) decreases with frequency.