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Resistor AC Characteristics · Voltage-Current Phase Difference

Apply a sinusoidal AC voltage \(v(t) = V_m \sin(2\pi f t)\) to a resistor and observe the phase relationship between voltage \(u(t)\) and current \(i(t)\)
Resistor current unit: milliamps (mA)

Signal Source & Resistor Parameters

1.00 V
0.2 V5 V
50.0 Hz
10 Hz500 Hz

Frequency does not affect the theoretical phase difference of a resistor (0°)

2.0 kΩ
0.1 kΩ10 kΩ

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

Resistor Phase Difference Theory

Resistor \(R\) \(\varphi = 0^\circ\) Voltage and current in phase
Expression: \(i_R = \frac{v}{R}\)
In sinusoidal steady-state, voltage and current are perfectly synchronized with no phase difference. Resistor current unit: mA
Current amplitude: \(I_{Rm} = \frac{V_m}{R} \times 1000\ \text{mA}\), convert \(R\) from kΩ to Ω when calculating.

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)

Waveform Observation Key Points

• Resistor: \(u_R\) and \(i_R\) cross zero simultaneously, peaks occur at the same time.
• Voltage and current waveforms perfectly overlap, differing only in amplitude.
• Adjusting resistor \(R\) changes current amplitude, but phase difference remains at \(0^\circ\).
• Resistor current unit: mA, convenient for observing small current cases.

Effect of Parameters on Amplitude

\(I_{Rm} = \frac{V_m}{R} \times 1000\ \text{(mA)}\)
Increase voltage \(V_m\) → current increases linearly;
Increase resistance \(R\) → current decreases linearly;
Frequency \(f\) does not affect resistor current amplitude.