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RC circuit charging
Intermediate
Capacitor voltage rises exponentially.
V = V₀(1−e^{−t/RC})After closing the switch a capacitor charges as V_C = V₀(1 − e^{−t/RC}); the current decays as I = (V₀/R)e^{−t/RC}.
R = 10 kΩ, C = 100 μF: τ = 1 s; after 1 s V_C = 63%.
Capacitor never fully charges in finite time.
In more detail
When a capacitor charges through a resistor, the voltage rises exponentially towards the supply voltage. The current starts high and falls to zero as the capacitor fills.
Real-world uses
- Timing circuits use RC charging to set delays.
- Camera flashes charge capacitors through resistors.
- A camera flash charges its capacitor through a resistor, and the voltage rises smoothly until the flash is ready.
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Frequently asked questions
What does the charging equation look like?
V = V0(1 − e^(−t/RC)).
Why does the current fall?
Because the voltage across the capacitor reduces the voltage available to drive current.
How long does a capacitor take to charge fully?
In practice, about five time constants, by which time the voltage is within one percent of its final value.
Related topics in Current Electricity & Circuits
Norton's theorem · Superposition theorem · Delta–star conversion · RC circuit discharging · Time constant · Current in RC circuit