Alternating Current
Alternating Current is a free interactive simulation from StudyFi Lab. It runs right in your browser, with no sign-up and nothing to install.
Sine waves, RMS, RLC circuits and a transformer
Experiments
Sine-wave voltage
An alternating voltage changes as u(t) = U_max·sin(ωt + φ), where ω = 2πf. It is the vertical projection of a phasor of length U_max turning at angular speed ω; one full turn takes the period T = 1/f. The effective (RMS) value U_rms = U_max/√2 heats a resistor just as much as a DC voltage of the same size — the 230 V of a socket is the RMS value, the peak is about 325 V.
Try this: Pick the Europe preset and compare U_max with U_rms, then switch to USA and watch the period get shorter.
R, L and C on AC
In a resistor the current is in phase with the voltage. In a coil the current lags 90° behind the voltage, and its reactance X_L = 2πfL grows with frequency. In a capacitor the current leads the voltage by 90°, and its reactance X_C = 1/(2πfC) falls with frequency. The current amplitude is I = U/X.
Try this: Choose the capacitor and raise the frequency: X_C drops, so the current grows. Then try the same with the coil.
Series RLC resonance
In a series RLC circuit the reactances subtract: the impedance is Z = √(R² + (X_L − X_C)²) and the voltage leads the current by φ = atan((X_L − X_C)/R). At the resonance frequency f₀ = 1/(2π√(LC)), X_L = X_C, so Z = R, φ = 0 and the current is at its largest. Above f₀ the circuit behaves inductively (φ > 0), below it capacitively (φ < 0).
Try this: Set f to f₀ — the voltages across L and C cancel, and each can be larger than the source voltage. Then increase R and watch the peak of the resonance curve get lower and wider.
Transformer
The alternating current in the primary coil creates a changing magnetic flux in the iron core, and this flux induces a voltage in the secondary coil. The voltages are in the ratio of the turns: U₂ = U₁·N₂/N₁. An ideal transformer loses no energy, so U₁·I₁ = U₂·I₂ — when the voltage goes up, the current goes down in the same ratio.
Try this: Make N₂ ten times N₁ — the voltage rises ten times, but the primary current is ten times the secondary one. This is why power is transmitted at high voltage.
Frequently asked questions
What is Alternating Current?
Alternating Current is a free interactive simulation from StudyFi Lab. It runs right in your browser, with no sign-up and nothing to install. Sine waves, RMS, RLC circuits and a transformer
Is Alternating Current free?
Yes. Alternating Current is completely free. It works in the browser on computers, tablets and phones, and you do not need an account.
What can I explore in Alternating Current?
Sine-wave voltage, R, L and C on AC, Series RLC resonance, Transformer.
What does the “Sine-wave voltage” experiment show?
An alternating voltage changes as u(t) = U_max·sin(ωt + φ), where ω = 2πf. It is the vertical projection of a phasor of length U_max turning at angular speed ω; one full turn takes the period T = 1/f. The effective (RMS) value U_rms = U_max/√2 heats a resistor just as much as a DC voltage of the same size — the 230 V of a socket is the RMS value, the peak is about 325 V.
What does the “R, L and C on AC” experiment show?
In a resistor the current is in phase with the voltage. In a coil the current lags 90° behind the voltage, and its reactance X_L = 2πfL grows with frequency. In a capacitor the current leads the voltage by 90°, and its reactance X_C = 1/(2πfC) falls with frequency. The current amplitude is I = U/X.
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