Formula & Calculator
Capacitor Charge Relation
Relates the charge stored on a capacitor to its capacitance and the voltage across it.
Interpretation
The charge stored on a capacitor is directly proportional to the voltage across it: Q = C·V.
This is the fundamental defining equation for capacitance.
Example: C=47µF, V=12V → Q = 47e-6 × 12 = 5.64×10⁻⁴ coulombs.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Formula | Q = C·V | |
| Q | Electric charge stored in capacitor | C (Coulombs) |
| C | Capacitance | F (Farads) |
| V | Voltage across capacitor | V (Volts) |
What it means
The fundamental relation for a capacitor is Q = C·V, where Q is the charge stored on one plate (in coulombs), C is the capacitance (in farads), and V is the voltage across the plates. This equation defines capacitance: the ratio of charge to voltage. It shows that for a given capacitor, the charge is proportional to the voltage. This relationship is derived from the definition of capacitance and is independent of the dielectric material. The charge stored is what determines the electric field and the energy stored (E = ½ QV). This relation is used in many circuit calculations, such as in RC circuits and in the design of sample‑and‑hold circuits. Understanding Q = CV is essential for analysing charge‑sharing in digital CMOS circuits and for designing charge‑pump voltage multipliers. Example: A 47µF capacitor with 12V across it stores Q = 47e-6 * 12 = 5.64×10⁻⁴ coulombs (564 µC).
Worked example
Capacitor Charge – Practical Example
Real‑World| Parameter | Value |
|---|---|
| C | 10 µF = 10×10⁻⁶ F |
| V | 50 V |
| Formula | Q = C · V |
Common mistakes
- Units: C in farads, V in volts → Q in coulombs.
- Charge on plates: The charge is proportional to voltage; the constant is capacitance.
- Sign: The charge sign depends on the polarity of the voltage.
- Discharging: During discharge, Q decreases as V drops.
- Definition: This is the defining equation for capacitance.
Applications
The charge stored on a capacitor, Q = C·V, is directly proportional to the voltage across it, with capacitance as the proportionality constant. This is the defining equation for capacitance and is used in many applications. Engineers use it to calculate the charge required for a given voltage, to design charge pumps, and to understand the operation of sample‑and‑hold circuits. In electrostatic discharge (ESD) protection, it helps estimate the charge transferred during an event. By using Q = CV, professionals can determine the current needed to charge a capacitor over time (I = C·dV/dt). This relationship is fundamental to all capacitive circuits and is a cornerstone of electronics.
- Capacitor charge and discharge time calculations
- Design of charge pumps and voltage multipliers
- Sample‑and‑hold circuit analysis
- ESD protection design and modelling
- Educational foundation of capacitance
Frequently Asked Questions
The charge stored on a capacitor is Q = C · V, where Q is in coulombs, C in farads, and V in volts.
Coulombs (C) when C is in farads and V in volts.
It is the amount of charge stored per unit voltage; C = Q/V.
For a fixed voltage, inserting a dielectric increases C, so Q increases (Q = CV).
Current is the rate of change of charge: I = dQ/dt.
Limited by the breakdown voltage; Q_max = C V_breakdown.
In series, the charge on each capacitor is the same and equals the total charge.
Designing capacitor banks, timing circuits, and energy storage systems.
The charge decreases exponentially: Q(t) = Q₀ e^(−t/RC).
Common errors include: 1) using the wrong units, 2) forgetting that Q is proportional to C, 3) applying the formula to non-linear capacitors, 4) confusing charge with voltage, and 5) using the formula for inductors.