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Inductor AC Characteristics · Voltage-Current Phase Difference

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

Signal Source & Inductor Parameters

1.00 V
0.2 V5 V
50.0 Hz
10 Hz500 Hz

Frequency affects inductive reactance, changing current amplitude; phase difference remains at +90°

2.0 mH
0.2 mH20 mH

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

Inductor Phase Difference Theory

Inductor \(L\) \(\varphi = +90^\circ\) Current lags voltage by \(90^\circ\)
Expression: \(i_L = \frac{1}{L}\int v\,dt\)
In sinusoidal steady-state, current lags voltage by \(90^\circ\). Inductor current unit: A
Current amplitude: \(I_{Lm} = \frac{V_m}{2\pi f L}\ \text{(A)}\), Inductive reactance \(X_L = \omega L = 2\pi f L\).

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)

Waveform Observation Key Points

• Inductor: current \(i_L\) zero-crossing lags voltage \(u_L\) by \(90^\circ\).
• Current is zero at voltage peak, voltage is zero at current peak.
• Adjusting frequency \(f\) or inductance \(L\) changes current amplitude, but phase difference remains at \(+90^\circ\).
• Inductor current unit: A, consistent with capacitor current unit.

Effect of Parameters on Amplitude

\(I_{Lm} = \frac{V_m}{2\pi f L}\ \text{(A)}\)
Increase voltage \(V_m\) → current increases linearly;
Increase frequency \(f\) → current decreases;
Increase inductance \(L\) → current decreases;
Inductive reactance \(X_L = \omega L\) increases with frequency.