Switching transients: RC, RL and series RLC

Throw a switch and watch charge flow, the capacitor fill and the inductor's field build. Every 0⁻, 0⁺ and ∞ value is tabulated, and the RLC roots move in the s-plane as you drag R.

t = 0⁻ (before the switch) · dots show current: their speed is |i|, and they reverse when i does.

R1 kΩC100 µF

Source before t = 00 VSource after t = 010 V

\tau = RC

= 100 ms5τ = 500 ms

Drag across a graph to move through time.

Voltages

v_C

= 0 V

v_R

= 0 V

Current

i

= 0 A

Initial and final values

The table GATE asks you to fill in. Highlighted cells jump at the switch.

	t = 0⁻	t = 0⁺	t → ∞	now (0⁻)
$v_C$	0 V	0 V	10 V	0 V
$v_R$	0 V	10 V	0 V	0 V
$i$	0 A	10 mA	0 A	0 A

What to notice

The capacitor voltage cannot jump: $v_C(0^+) = v_C(0^-) = 0\,\text{V}$ .
The current does jump, from $0$ to $\dfrac{V_{after} - v_C(0^+)}{R} = 10\,\text{mA}$ .
$\tau = RC = 100\,\text{ms}$ . After $\tau$ , $63.2\%$ of the change is done; after $5\tau$ , $99.3\%$ .
At $t \to \infty$ the capacitor is an open circuit: $i = 0$ , $v_C = 10\,\text{V}$ .

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