RC Circuits

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📘 RC Circuits

Textbook

University Physics Volume 2: Chapter 10.5 - RC Circuits

What is a Capacitor and what is Capacitance

See Capacitors

Theory

Capacitor Charging (Voltage over Time)

During charging, the voltage across a capacitor increases exponentially, approaching its final value.

$V(t)=V_0(1-e^{-\frac{t}{RC}})$

Where:

• $V(t)$ is the voltage at time t (in volts, V).
• $V_0$ is the final voltage (in volts, V).
• $R$ is the resistance (in ohms, Ω).
• $C$ is the capacitance (in farads, F).
• $t$ is time (in seconds, s).

Charge

$q(t)=C{V}_0(1-e^{-\frac{t}{RC}})$

Current

$i(t)=\frac{dq}{dt}=\frac{V_0}{R}{e}^{-\frac{t}{RC}}$

Capacitor Discharge (Voltage over Time)

During the discharge of a capacitor through a resistor, the voltage decreases exponentially over time.

$V(t)=V_0{e}^{-\frac{t}{RC}}$

Where:

• $V(t)$ is the voltage at time t (in volts, V).
• $V_0$ is the initial voltage (in volts, V).
• $R$ is the resistance (in ohms, Ω).
• $C$ is the capacitance (in farads, F).
• $t$ is time (in seconds, s).

Charge

$q(t)=C{V}_0{e}^{-\frac{t}{RC}}$

Current

$i(t)=\frac{dq}{dt}=-\frac{V_0}{R}{e}^{-\frac{t}{RC}}$

Example Graphs

Videos

▶ Watch video 1 on YouTube

▶ Watch video 2 on YouTube

Simulations

• PhET Circuit Construction Kit

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