Question 1

What is the RC time constant?

Accepted Answer

The time constant τ = RC is the time for a capacitor to charge to approximately 63.2% (1 − 1/e) of the final voltage. After 5τ it is effectively fully charged (99.3%). The unit of R (ohms) × C (farads) is seconds. For example, R = 10 kΩ and C = 100 μF gives τ = 1 s.

Question 2

How is the energy stored in a capacitor calculated?

Accepted Answer

The energy stored in a capacitor is U = ½CV², where C is the capacitance in farads and V is the voltage. At full charge U_max = ½CV₀². Using Q = CV, the energy can also be written as U = Q²/(2C).

Question 3

How does the voltage change during discharge?

Accepted Answer

A fully charged capacitor (initial voltage V_i) discharging through R follows V_C(t) = V_i·e^(−t/RC). The current is I(t) = −(V_i/R)·e^(−t/RC) (negative sign indicates discharge direction). After one time constant τ the voltage falls to about 36.8% (1/e) of the initial value.

Question 4

What engineering designs is this simulator useful for?

Accepted Answer

Key applications include: (1) power-supply filter design (cutoff frequency f_c = 1/(2πRC)), (2) flash/strobe energy calculations, (3) pulse-power charge/discharge timing, and (4) quick hand-verification before building SPICE models. The AC mode directly shows the relationship between frequency and capacitor impedance.

Capacitor Charge/Discharge & Energy Simulator

Theory