Charging capacitor Calculator
Voltage across a charging capacitor.
Formula first
Overview
This equation models the exponential rise of voltage across a capacitor as it accumulates charge through a resistor. It defines the transient behavior of an RC circuit, where the charging rate is determined by the time constant product of resistance and capacitance.
Symbols
Variables
= Supply Voltage, t = Time, R = Resistance, C = Capacitance, V(t) = Capacitor Voltage
Apply it well
When To Use
When to use: Apply this formula when analyzing a series RC circuit connected to a constant DC voltage source. It assumes the capacitor starts with zero initial charge and that components behave ideally throughout the charging process.
Why it matters: Understanding capacitor charging is critical for designing timing circuits, signal filters, and power-on reset mechanisms. It allows engineers to predict how long a system takes to reach a specific logic level or operating threshold.
Avoid these traps
Common Mistakes
- Using base⁻10 exponent instead of e.
- Using t in ms while RC in s.
One free problem
Practice Problem
A 12V battery is connected to a 100 µF capacitor through a 10 kΩ resistor. Calculate the voltage across the capacitor after 1 second of charging.
Solve for: Vt
Hint: Calculate the time constant (RC) first, then plug it into the exponential part of the formula.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Halliday, Resnick, Walker, Fundamentals of Physics, 10th Edition
- Wikipedia: RC circuit
- Halliday, Resnick, Walker, Fundamentals of Physics, Extended
- IUPAC Gold Book
- Halliday, Resnick, and Walker Fundamentals of Physics
- Nilsson and Riedel Electric Circuits
- OCR A-Level Physics — Capacitance