Charging and Discharging of a Capacitor

Charging and Discharging of a Capacitor

What is it?

In an RC circuit, a capacitor charges or discharges exponentially rather than instantaneously because resistance limits the flow of charge.

In simple words

• RC circuits change exponentially with characteristic time `RC`.

Full school-level explanation

In an RC circuit, a capacitor charges or discharges exponentially rather than instantaneously because resistance limits the flow of charge.

Charging

Consider resistor `R` and capacitor `C`. The characteristic timescale is: τ=RC called the time constant. Connected to a battery of emf `V₀`: q(t)=CV₀(1−e⁽−t/RC)) Capacitor voltage: V_C(t)=V₀(1−e⁽−t/RC)) Current: I(t)=V₀R · e^(−t/RC) At `t=0`: `q=0` `V<sub>C</sub>=0` current is maximum. As `t→∞`: `q→CV₀` `V_C→V₀` `I→0`.

Discharging

For initial charge `Q₀`: q(t)=Q₀e⁽−t/RC) V_C(t)=V₀e⁽−t/RC) Current magnitude decreases exponentially.

At One Time Constant

Charging: approximately 63% of final charge/voltage. Discharging: approximately 37% remains. The textbook's current Chapter 19 structure explicitly includes charging and discharging as its own section. ([Sabaq Foundation][2])

Formula / Key Relation

**τ=RC** Charging: **V_C=V₀(1−e⁽−tτ))** Discharging: **V_C=V₀e⁽−tτ)**

Remember

• q(t)=CV₀(1−e⁽−t/RC))
• V_C(t)=V₀(1−e⁽−t/RC))
• I(t)=V₀R · e⁽−t/RC)
• q(t)=Q₀e⁽−t/RC)
• V_C(t)=V₀e⁽−t/RC)
• 63%
• 37%
• τ=RC

Deeper understanding

Go deeper on Charging and Discharging of a Capacitor: connect the definition to reasons, relationships, exceptions, and exam wording.

Common mistakes

Exam focus

RC

Exam focus

Quick revision

• q(t)=CV₀(1−e⁽−t/RC))
• V_C(t)=V₀(1−e⁽−t/RC))
• I(t)=V₀R · e⁽−t/RC)
• q(t)=Q₀e⁽−t/RC)
• Charging: Consider resistor `R` and capacitor `C`. The characteristic timescale is: τ=RC called the **t
• Discharging: For initial charge `Q₀`: q(t)=Q₀e⁽−t/RC) V_C(t)=V₀e⁽−t/RC) Current magnitude decreases

For long answers on Charging and Discharging of a Capacitor: define clearly → explain the main parts → give one example → state one exam caution.