An RC circuit is a simple electrical circuit made from a resistor and a capacitor connected to a voltage source. It is important because it shows how electrical energy can be stored, released, and controlled over time. Engineers use RC circuits in timers, sensors, camera flashes, audio electronics, and signal filters.
The key idea is that voltage and current do not change instantly because the capacitor must charge or discharge through the resistor.
The behavior of an RC circuit is governed by the time constant tau = RC, where R is resistance in ohms and C is capacitance in farads. During charging, the capacitor voltage rises exponentially toward the source voltage V0, while the current starts large and decreases toward zero. During discharging, the capacitor voltage falls exponentially from its initial value toward zero.
This same exponential behavior helps engineers design delay circuits and filters that pass or block signals depending on frequency.
Key Facts
- Time constant: tau = RC
- Charging capacitor voltage: VC(t) = V0(1 - e^(-t/RC))
- Discharging capacitor voltage: VC(t) = Vinitial e^(-t/RC)
- Charging current: I(t) = (V0/R)e^(-t/RC)
- After one time constant, a charging capacitor reaches about 63% of V0 and a discharging capacitor falls to about 37% of its initial voltage.
- Capacitor charge is related to voltage by Q = CV.
Vocabulary
- RC circuit
- A circuit containing a resistor and a capacitor whose voltage and current change over time.
- Capacitor
- A component that stores electric charge and energy in an electric field between two conducting plates.
- Time constant
- The quantity tau = RC that sets how quickly the capacitor charges or discharges.
- Exponential decay
- A pattern of decrease where a quantity falls by the same fraction during each equal time interval.
- Filter
- A circuit that changes a signal by allowing some frequency ranges to pass more easily than others.
Common Mistakes to Avoid
- Treating the capacitor voltage as changing instantly is wrong because a capacitor needs time to gain or lose charge through the resistor.
- Forgetting the units in tau = RC is wrong because ohms times farads gives seconds, so tau must be interpreted as a time.
- Using the charging equation for a discharging situation is wrong because charging approaches V0 while discharging approaches 0 V.
- Assuming the current stays constant is wrong because the current is largest at the start and decreases exponentially as the capacitor voltage changes.
Practice Questions
- 1 A 10 kOhm resistor is connected in series with a 100 microfarad capacitor. Calculate the time constant tau.
- 2 A capacitor charges from a 12 V battery through a resistor. What is the capacitor voltage after one time constant?
- 3 Explain why increasing the resistance in an RC timing circuit makes an LED stay on or off for a longer time.