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Pure Component AC Characteristics · Voltage-Current Phase Difference

Apply the sinusoidal AC voltage \(v(t) = V_m \sin(2\pi f t)\) to \(R\), \(L\), and \(C\) components and compare their voltage-current phase relationships
Resistor current: milliamps (mA)  |  Inductor/Capacitor current: amperes (A)

Signal Source & Component Parameters

1.00 V
0.2 V5 V
50.0 Hz
10 Hz500 Hz

Frequency affects inductive/capacitive reactance but does not change the theoretical phase difference (±90°)

1.0 kΩ
0.1 kΩ10 kΩ

Resistor voltage and current are in phase, current amplitude \(I_m = V_m / R\) (mA)

2.0 mH
0.2 mH20 mH

Current lags voltage by \(90^\circ\), amplitude \(I_m = V_m / (\omega L)\) (A)

2000 μF
1000 μF5000 μF

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

Phase Difference Theory Quick Reference

Resistor \(R\) \(\varphi = 0^\circ\) Voltage and current in phase
Inductor \(L\) \(\varphi = +90^\circ\) Current lags voltage by \(90^\circ\)
Capacitor \(C\) \(\varphi = -90^\circ\) Current leads voltage by \(90^\circ\)
Expressions: \(i_R = \frac{v}{R}\), \(i_L = \frac{1}{L}\int v\,dt\), \(i_C = C\frac{dv}{dt}\)
In sinusoidal steady-state, inductor current lags, capacitor current leads. Resistor current in mA, Inductor/Capacitor current in A

Resistor · Voltage \(u_R(t)\) and Current \(i_R(t)\) (mA)

Phase Diff \(\Delta\varphi = 0^\circ\) (In Phase)
Ohm's Law: current waveform perfectly overlaps voltage waveform with no phase shift (current unit: mA)

Inductor · Voltage \(u_L(t)\) and Current \(i_L(t)\) (A)

Phase Diff \(\Delta\varphi = +90^\circ\) (Current Lags)
Inductive component: current lags voltage by 90°, \(i_L(t)\) peak occurs \(\frac{T}{4}\) after voltage peak (current unit: A)

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

• Resistor: \(u_R\) and \(i_R\) cross zero simultaneously, peaks occur at the same time.
• Inductor: current \(i_L\) zero-crossing lags voltage \(u_L\) by \(90^\circ\) (current is zero at voltage peak).
• Capacitor: current \(i_C\) zero-crossing leads voltage \(u_C\) by \(90^\circ\) (voltage is zero at current peak).
• Adjusting frequency \(f\), inductance \(L\), capacitance \(C\) changes current amplitude, but phase difference remains at theoretical value.
• Resistor current in mA, Inductor/Capacitor current in A, for easy amplitude comparison on the same coordinate system.

Effect of Parameters on Amplitude

\(I_{Lm} = \frac{V_m}{2\pi f L}\ \text{(A)}\), \(I_{Cm} = V_m \cdot 2\pi f C\ \text{(A)}\).
Increase frequency \(f\) → inductor current decreases, capacitor current increases;
Increase \(L\) → inductor current decreases; Increase \(C\) → capacitor current increases.
Resistor current \(I_{Rm}= \frac{V_m}{R} \times 1000\ \text{mA}\), convert \(R\) from kΩ to Ω when calculating.