RC Circuits
Introduced| English |
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| RC circuit/ˌɑː ˈsiː ˈsɜːkɪt/ |
A capacitor charges fast at first, then dawdles
- Connect a capacitor through a resistor and it charges quickly at first, then slower and slower.
- It never quite reaches full charge — it just creeps closer and closer.
- A resistor + capacitor circuit is an RC circuit RC电路, and it introduces time into circuits.
- These circuits time windscreen wipers, camera flashes and the blink of an LED.
Charging is exponential
- As a capacitor charges through a resistor, its charge rises toward a final value $Q = CV$.
- The rise is exponential: fast at first (big current), slowing as the capacitor fills.
- The current falls as the charge grows — when full, no more current flows.
- Discharging is the mirror image: charge falls exponentially toward zero.
Charge through a resistor
Change R and C and watch the charging curve speed up or slow down.
As a capacitor charges through a resistor, its charge rises:
Charge rises exponentially toward $Q = CV$, fast at first then slowing.
The time constant
- The time constant $\tau = RC$ sets how fast the circuit charges or discharges.
- After one time constant, the capacitor reaches about $63\%$ of its final charge.
- A bigger resistance or capacitance means a slower (longer) charge.
- Change $R$ or $C$ and you tune the timing — that is how RC timers work.
An RC circuit has $R = 2\ \Omega$ and $C = 3\ \text{F}$. What is the time constant, in seconds?
$\tau = RC = 2 \times 3 = 6\ \text{s}$.
The time constant of an RC circuit is $\tau = R \times \_\_$.
$\tau = RC$ — resistance times capacitance.
Increasing the resistance in an RC circuit makes the charging:
A bigger $R$ gives a bigger $\tau = RC$, so slower charging.
Why the resistor matters
- The resistor limits the current, so it controls how fast charge flows onto the plates.
- With no resistance the capacitor would charge instantly (an idealisation).
- With a large resistance, charging takes a long, gentle time.
- So $R$ and $C$ together set the circuit's natural "clock".
Select all true statements about RC circuits.
RC circuits charge exponentially with $\tau = RC$; bigger R or C is slower. Charging is never instant.
A charging capacitor never reaches its final charge in a finite time — it only approaches it exponentially. After one time constant it is at $\approx 63\%$, not $100\%$. "Fully charged" really means "close enough after several time constants".
A charging capacitor reaches exactly 100% of its final charge after one time constant.
After one time constant it is at about $63\%$; it only approaches $100\%$ over several $\tau$.
An RC circuit has $R = 2\ \Omega$ and $C = 3\ \text{F}$. What is its time constant?
- $\tau = RC = 2 \times 3 = 6\ \text{s}$.
After $6\ \text{s}$ the capacitor holds about $63\%$ of its final charge; after several $\tau$ it is essentially full.
An RC circuit (resistor + capacitor) charges and discharges exponentially over time. The time constant $\tau = RC$ sets the speed: after one $\tau$ the charge is $\approx 63\%$ of its final value $Q = CV$. Bigger $R$ or $C$ means slower timing — the basis of electronic timers.