Engineering Theory & Mathematical Model
When the SPDT switch connects the resistor R (470 Ω) to the 10V DC supply, current initially surges at I₀ = V₀/R = 21.28 mA because an uncharged capacitor acts like an instantaneous short circuit. As charge accumulates on the plates, capacitor voltage rises exponentially, reaching 63.2% of V₀ after one time constant τ = RC (22.1 ms) and >99.3% after 5τ. Flipping the SPDT switch to ground reverses current direction and discharges stored electrostatic energy ½CV² as heat in R.
Interactive Lab Procedure
- Click the SPDT switch (CHG/DIS) directly on the canvas to alternate between 10V charging and 0V discharging.
- Observe the sky-blue CH1 trace on the oscilloscope plotting the exact exponential curve Vc(t) alongside the amber charging current CH2.
- Select C1 (47 µF) or R1 (470 Ω) in the Inspector to double resistance and watch the time constant τ stretch in real time.
Technical FAQ
What is the core governing formula for RC Capacitor Charge & Discharge Simulator (SPDT Switch)?
Vc(t) = V0 × (1 − e^(−t / RC)), τ = R × C = 22.09 ms — When the SPDT switch connects the resistor R (470 Ω) to the 10V DC supply, current initially surges at I₀ = V₀/R = 21.28 mA because an uncharged capacitor acts like an instantaneous short circuit. As charge accumulates on the plates, capacitor voltage rises exponentially, reaching 63.2% of V₀ after one time constant τ = RC (22.1 ms) and >99.3% after 5τ. Flipping the SPDT switch to ground reverses current direction and discharges stored electrostatic energy ½CV² as heat in R.
Can I modify component values and rewire this circuit live?
Yes! The schematic above runs a live MNA SPICE engine. Click any part to adjust parameters, add or delete wires and components, and click Share URL to save your custom topology.