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Physics
Capacitor laboratory
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A parallel-plate capacitor connected to a battery through switch K. Change the battery voltage, the plate area and the plate separation to see how capacitance, charge, electric field and stored energy change; in Light bulb mode, let the capacitor discharge through a bulb.
Connected to the battery: the voltage between the plates always equals the battery voltage. Changing S or d changes C, so Q = C·U changes too; current flows in the wires while Q changes.
- CapacitanceC = ε₀S/d
- 0.295 pF
- Voltage between the platesU = U battery
- 1.50 V
- Top plate chargeQ = C·U
- 0.443 pC
- Electric field strengthE = U/d
- 250 V/m
- Stored energyW = ½·C·U²
- 0.332 pJ
Vacuum capacitor (ε = 1), ε₀ = 1/(4πk) ≈ 8.85·10⁻¹² F/m, so C = ε₀S/d is the same as C = εS/(4πkd).
Model notes
- The parallel-plate capacitor has two square metal plates facing each other in vacuum (ε = 1). Its capacitance is C = ε₀S/d with ε₀ ≈ 8.85·10⁻¹² F/m; since ε₀ = 1/(4πk), this is the same formula as C = εS/(4πkd). Edge effects are ignored: the field between the plates is uniform, E = U/d, and zero outside.
- The plates are only 10–20 mm wide and 2–10 mm apart, so the capacitance is only about 0.09–1.8 picofarads (1 pF = 10⁻¹² F); charge is shown in picocoulombs (pC) and energy in picojoules (pJ). Capacitors in real circuits are millions of times larger thanks to large areas, tiny gaps and dielectrics.
- When connected to the battery, the voltage between the plates equals the battery voltage at once: the model ignores wire resistance and charging time. With the circuit open the charge has nowhere to go and stays the same; then changing S or d changes C, and therefore U = Q/C and W = Q²/(2C).
- The bulb has an illustrative resistance R = 5·10¹² Ω, far larger than a real bulb, so that the discharge time τ = RC is about a second and can be watched. The bulb current is only a few tenths of a picoampere, so a real bulb would not glow; the glow here simply grows with the current. When the voltage between the plates drops below 1 mV, the model treats the capacitor as fully discharged.
- The number of + and − signs on the plates and the number of field lines grow with the size of the charge; they are only a qualitative picture: one sign is not one electron. The real charge sits on the inner faces of the plates (the faces looking at each other); the signs are drawn on the top face of each plate so that they can be seen.
- Current arrows show the conventional direction by default (the direction positive charge would move); choosing electrons reverses the arrows because electrons are negative. With the battery connected, current flows only while the charge is changing, so the arrows appear briefly and then fade.