Electromagnetism
Same C in a circuit
This plate geometry gives the same C as the RC charging preset in Circuits — open it to watch Q(t).
Same C in a circuit — interactive Electromagnetism simulation. This plate geometry gives the same C as the RC charging preset in Circuits — open it to watch Q(t). Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Capacitance in circuits
This plate geometry gives the same C as the RC charging preset in Circuits — open it to watch Q(t).
This parallel-plate geometry uses area A and separation d so C = ε₀A/d matches the RC charging preset in Circuits. The overlay schematic shows V–R–C in series with the computed µF value. Press Play to watch the field build; open the linked Circuits preset to see Q(t) = CV(1 − e^(−t/RC)) for the same C.
- C = ε₀A/d
- Q = CV
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
The rc-charging circuit experiment uses an idealized 0.01 F capacitor. Building a real parallel-plate capacitor with that much capacitance would need an impossibly small gap for a vacuum — unless you stack many thin dielectric layers. Does adding more layers increase or decrease the total capacitance?
Predictions to weigh
- More layers decrease capacitance.
- More layers increase capacitance — it's like stacking several capacitors' worth of charge storage in parallel.
- Layer count doesn't affect capacitance, only the dielectric material does.
Variable roles
What you set:
- Layer count N
What you measure:
- Capacitance C (mF)
How the investigation runs
- Open the plate-same-c-in-circuit preset and press Reset. This capacitor uses a high-k dielectric (εr = 1000) to physically realize the same 0.01 F as the rc-charging circuit experiment.
- Enable the capacitance readout.
- For each trial, use the given layer count (area, separation, and εr held fixed at this experiment's actual values) to compute the resulting capacitance.
Governing equation
Multilayer Capacitance — C = ε₀A/d
Interleaving N layers of dielectric between plates multiplies the single-layer capacitance by N: C = ε₀εrAN/d. This is how real capacitors reach large capacitance values in a compact size.
What the printable worksheet asks students to work out
- For one trial, compute C = ε₀εrAN/d using ε₀ = 8.854×10⁻¹² F/m, εr = 1000, A = 0.01 m², d ≈ 8.854 µm (this experiment's fixed separation). Compare to the table. Confirm that N = 1000 reproduces the linked circuit's 0.01 F exactly.
- Explain why interleaving more layers of dielectric (like a real multilayer ceramic capacitor) multiplies the effective capacitance, the same way stacking capacitors in parallel would.
Where this shows up beyond the lab
- Real 0.01 F ('10,000 µF') capacitors exist as compact components you can hold in your hand, thanks to exactly this trick: extremely thin, tightly rolled or stacked layers of high-permittivity dielectric between huge effective plate areas. Explain why a naive single-layer vacuum-gap design could never achieve this in a small package.
- This capacitor's voltage is set to match the rc-charging circuit experiment's battery EMF exactly. Why might it be useful, when teaching capacitors, to show the same numeric capacitance built two different ways — as an idealized circuit symbol and as a physically realizable multilayer device?
- AP Physics 2 — Unit 10: Electric Force, Field, and Potential
- AP Physics C: Electricity and Magnetism — Unit 10: Conductors and Capacitors
- IB Physics — D.2 Electric and magnetic fields
- General High School Physics — Magnetism & electromagnetism
- NGSS High School Physics — Energy in particle motion and fields
- Welcome to Plate Same C In Circuit
- Select the capacitor
- Press Play
- Capacitance in a circuit
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.