Charging and discharging of capacitor - Physics - eSaral

eSaral Academic and Editorial Team
Hey, do you want to learn about the Charging and discharging of capacitors? If yes. Then you are at the right place.
Charging and discharging of capacitors
Charging
When a capacitor C is connected to a battery through R then charging of capacitor takes place.

The eqn. of emf at any time t is
$R I+\frac{q}{C}=E$
$\frac{R d q}{d t}+\frac{q}{C}=E$
$\int_{0}^{Q} \frac{d q}{(C E-q)}$
$=-\int_{0}^{t} \frac{d t}{R C}$
This on solving gives $Q=Q_{0}\left(1-e^{-t / R C}\right)$
where $Q_{0}=C E$
Important Points
- The charge on a capacitor increases exponentially with time

- The current during charging process is$I=\frac{d Q}{d t}$$=-\frac{Q_{0}}{R C} e^{-t / R C}$$=-I_{0} e^{-t / R C}$
The current decreases exponentially with time.

- $\tau=R C$ is the capacitive time constant. It is the time in which the charge on the capacitor reaches 0.632 times of its maximum value during charging.
- The time constant is the time in which current reduces to $\frac{1}{\mathrm{e}}$ times or 0.368 times of its initial value
- At initial time $\mathrm{t}=0$ and $I=I_{\max }$ so circuit acts as short circuit or conducting wire.At $t=\infty \quad I=0$ so circuit acts as an open circuit or as a broken wire.
- The voltage increases exponentially with time as $V=V_{0}\left(1-e^{-t / R C}\right)$ during charging.
Discharging
If a completely charged capacitor C having charge $\mathrm{Q}_{0}$ is discharged through a resistance R then equation of emf at any time t is
$\mathrm{RI}+\frac{\mathrm{q}}{\mathrm{C}}=0$
Or
$R \frac{d q}{d t}+\frac{q}{C}=0$
Or
$\int_{Q_{0}}^{Q} \frac{d q}{q}=-\int_{0}^{t} \frac{d t}{R C}$
Or
$Q=Q_{0} e^{-t / R C}$
Important Points
- During discharging charge on a capacitor decreases exponentially with time.

- The current during discharging process$I=\frac{d Q}{d t}=-\frac{Q_{0}}{R C} e^{-t / R C}$$=-I_{0} e^{-t / R C}$
The current decreases exponentially with time. - Time constant is the time in which charge on capacitor become $\frac{1}{\mathrm{e}}$ or 0.368 times of its initial value $\mathrm{Q}_{0}$
- Time constant is the time in which current reduces to $\frac{1}{\mathrm{e}}$ or 0.368 times of its initial value $\mathrm{I}_{0}$.The direction discharging current is opposite to that of charging.
- During discharging voltage decreases with time as $V=V_{0} e^{-t / R C}$
so, that's all from this article. I hope you get the idea about the Charging and discharging of capacitors. If you found this article informative then please share it with your friends. If you have any confusion related to this topic then feel free to ask in the comments section down below.
For a better understanding of this chapter, please check the detailed notes of Electrostatics. To watch Free Learning Videos on physics by Saransh Gupta sir Install the eSaral App.

Team eSaral
eSaral Academic and Editorial Team
Team eSaral is the collective author profile for educational content created by eSaral’s teachers and academic contributors. The team draws on expertise from IIT graduates, doctors, experienced educators and subject specialists to develop resources for JEE, NEET and school students. Our articles aim to explain concepts clearly and help students study with confidence.
Related Posts

Plant Cell Diagram: Labelled Structure, Parts and Functions
Simple, labelled plant cell diagram with parts and functions. Covers plant cell structure for Class 6, 7, 8, 9, 10 and 11 students, CBSE-aligned.

Saransh Gupta Sir's Visit to IIT Patna: Hostel Life, Placements & Lessons for JEE Aspirants
Inside Saransh Gupta Sir's IIT Patna visit — hostel life, the library, placements, internships, and real advice for JEE aspirants from students living the IIT dream.

Molality Formula: Formula for Molality, Derivation & Solved Examples
Molality formula is $m = \dfrac{n}{W}$. Learn the formula of molality, its SI unit, derivation, relation with molarity, and solved examples for Class 11, JEE and NEET.

BITSAT Previous Year Question Paper PDF
Download BITSAT previous year question papers PDF. Get year-wise BITSAT PYQs, memory-based papers, exam pattern, and preparation tips to improve your BITSAT preparation.

Teachers’ Day 2026 at eSaral Gurukul: Celebrating the Bond Between Students, Teachers & Mentors
See how Teachers’ Day 2026 was celebrated at eSaral Gurukul, reflecting the bond among students, teachers, and mentors, and the role of guidance beyond academics.

JEE Advanced Attempts: Can You Give It a Third Time? Rules Explained
JEE Advanced attempts: current rule is 2 consecutive years only: full eligibility criteria, the 2025 third-attempt controversy, and the latest 2026 petition news.

Best JEE Preparation App
Best JEE preparation app for Main & Advanced: AI mock tests, live doubt-solving, thousands of practice questions. JEE preparation app for droppers & Class 11-12.

Coordinate Geometry Class 10: Formulas, Notes & Solved Examples
Coordinate geometry class 10: complete CBSE formulas — distance, section, midpoint and area of triangle — with derivation, notes and solved examples.

How to make Notes For JEE Smart Notes Strategy of an AIR 41
Learn how to make notes for JEE the way toppers do — indexing, shorthand, and smart short notes for JEE that cut revision time to just 5–7 days.

SL Arora Physics Class 12 Index – Chapter List for Volume 1 & 2
SL Arora Physics Class 12 index — complete chapter list for Volume 1 & 2, mapped to NCERT solutions for board, JEE Main, and NEET preparation.
