RC Circuit Calculator

What Is an RC Circuit?

An RC circuit pairs a resistor and capacitor in series with a voltage source. When the switch closes, the capacitor charges through the resistor. Current is highest at the start and falls exponentially as the capacitor fills. Voltage across the capacitor rises toward the source voltage following the same exponential curve.

RC Charging Formulas

The time constant defines how fast the circuit responds:

$$\tau = RC$$

Capacitor voltage and current at time $t$ are:

$$V(t) = V_0\left(1 - e^{-t/\tau}\right)$$ $$I(t) = \frac{V_0}{R} e^{-t/\tau}$$

After one time constant, the capacitor reaches about 63.2% of the source voltage. After five time constants it is effectively fully charged.

Practical Uses

RC circuits appear in timing circuits, filter networks, camera flashes, and debounce circuits. Engineers pick R and C values to set the desired charge time or cutoff frequency.

Frequently Asked Questions

What is the RC time constant?

The time constant tau equals resistance times capacitance (RC). It measures how quickly the capacitor charges. After one tau, the capacitor holds about 63.2% of the source voltage.

How long does an RC circuit take to fully charge?

Charging is exponential, so it never reaches 100% in finite time. In practice, five time constants (5RC) brings the capacitor to about 99.3% of the source voltage.

Why does current decrease during charging?

As the capacitor voltage rises, the voltage difference across the resistor shrinks. Less voltage across R means less current by Ohm's law, so current follows an exponential decay.

What units should I use for capacitance?

Use farads (F) in the formula. Microfarads (uF) and nanofarads (nF) are common in practice. The calculator accepts F, mF, uF, nF, and pF and converts internally.

Does this calculator handle discharging?

This tool focuses on charging from zero. Discharging follows V(t) = V0 * e^(-t/RC) with the same time constant tau = RC.

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What Is an RC Circuit?

RC Charging Formulas

Practical Uses

Frequently Asked Questions

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