Series RLC Circuit and Resonance
PhysicsElectricity & CircuitsAges 17–18Virtual lab
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Electricity & Circuits
A series R, L, C circuit driven by an AC voltage: graphs of u and i show their phase difference, alongside a phasor diagram and a curve of current versus frequency. Adjust L, C, or the frequency until Z_L = Z_C, the current reaches its maximum, and u falls in phase with i — this is electrical resonance, the principle behind tuning a radio. The Free LC oscillations screen connects a charged capacitor to the coil: energy swaps between ½Cu² and ½Li² with T = 2π√(LC), beside a mass–spring analogue; a resistance gives underdamped, critical or overdamped discharges, and a maintenance circuit keeps the oscillations going.
Lesson: Alternating Current
What it shows
In a series RLC circuit driven by an alternating voltage, the reactances Z_L = ωL and Z_C = 1/(ωC) change in opposite directions as the frequency rises, and the impedance is Z = √(R² + (Z_L − Z_C)²). At the resonant frequency f₀ = 1/(2π√(LC)) they cancel, Z equals R, the current peaks and u and i are in phase; R only sets how sharp the peak is. The Free LC oscillations screen connects a charged capacitor to the coil: energy swaps between ½Cu² and ½Li² with T = 2π√(LC), like a mass on a spring, and a resistance gives underdamped, critical or overdamped discharges.
How to use
On the AC resonance tab, change f slowly and watch the phase shift between u and i, press Tune f to resonance, then change L, C or R to move or sharpen the peak. On the Free LC oscillations tab, press Run and then Measure T; repeat for several values of Inductance L and Capacitance C and plot T against √(LC). Raise Resistance R to find the critical discharge, or tick Maintenance circuit (−R) to keep the oscillations going.
Parameters you can change
- Starting screen AC resonance, Free LC oscillations
- Frequency 10–200 Hz
- Resistance R 5–200 Ω
- Inductance L 10–600 mH
- Capacitance C 5–200 µF
- Free LC screen: resistance R 0–1000 Ω
- Free LC screen: charging voltage U₀ 1–12 V
- Free LC screen: maintenance circuit on
Questions to explore
- If the capacitance is made four times larger, how does the resonant frequency change?
- How can you tell from the phasor diagram whether the circuit is inductive or capacitive?
- How does lowering R change the height and width of the resonance peak, and does f₀ move?
