Capacitor Calculator

About Capacitor Calculator

Capacitors store charge Q = CV. Energy stored = ½CV². Time constant τ = RC.

How to use this calculator

1. Choose the quantity you want to find, such as charge, voltage, or capacitance.
2. Enter the values you know, making sure the units are consistent, like \( C\) for charge, \(V\) for voltage, and \(F\) for capacitance.
3. Use \(Q = CV\) to connect charge, capacitance, and voltage.
4. If you need stored energy, use \(E = \frac{1}{2}CV^2\).

The formula explained

The formula \(Q = CV\) computes the charge stored on a capacitor. The formula \(E = \frac{1}{2}CV^2\) computes the energy stored in the electric field of the capacitor.

• Q = charge stored on the capacitor, measured in coulombs \(\text{C}\)
• C = capacitance, measured in farads \(\text{F}\)
• V = voltage across the capacitor, measured in volts \(\text{V}\)
• E = stored energy, measured in joules \(\text{J}\)

Step by step method

1. Write down the known values for \(Q\), \(C\), or \(V\), and make sure the units match.
2. Use \(Q = CV\) and rearrange it if needed, so \(C = \frac{Q}{V}\) or \(V = \frac{Q}{C}\).
3. If the question asks for energy, substitute your values into \(E = \frac{1}{2}CV^2\).

Worked example

Problem. A capacitor has a capacitance of \(C = 4.0 \, \text{F}\) and a voltage of \(V = 3.0 \, \text{V}\). Find the charge and the stored energy.

1. Use \(Q = CV\), so \(Q = (4.0)(3.0) = 12\).
2. The charge is \(Q = 12 \, \text{C}\).
3. Use \(E = \frac{1}{2}CV^2\), so \(E = \frac{1}{2}(4.0)(3.0)^2 = 18\).

Tips and common mistakes

• Check your units before calculating, because \(Q = CV\) only works directly when \(Q\) is in coulombs, \(C\) is in farads, and \(V\) is in volts.
• Remember that voltage is squared in \(E = \frac{1}{2}CV^2\), so doubling the voltage makes the stored energy four times larger.

Frequently asked questions