19.1 Capacitors and Capacitance

1. What is a Capacitor?

A capacitor is an electrical component that stores energy. It is made of two parallel metal plates separated by an insulating material (called a dielectric — an insulator that stops charge from flowing directly between the plates).

When a capacitor is connected to a battery:

• The positive terminal of the battery pulls electrons away from one plate, leaving it with a positive charge.
• The negative terminal of the battery pushes electrons onto the other plate, giving it a negative charge.
• The two plates end up with equal but opposite charges, for example +Q on one plate and −Q on the other.

Important point: The net (overall) charge of the capacitor is always zero, because +Q and −Q cancel out. However, work is done by the battery to separate those charges, and that work is stored as electrical energy in the capacitor.

2. Defining Capacitance

For a Parallel Plate Capacitor

When you increase the voltage (potential difference) across a capacitor's plates, more charge builds up on the plates. Experiment shows that charge Q is directly proportional to voltage V:

$Q \propto V \implies Q = CV$

The constant C in this equation is called the capacitance of the capacitor.

In equation form:

$\boxed{C = \frac{Q}{V}}$

Where:

• C = capacitance, measured in farads (F)
• Q = charge stored on one plate, measured in coulombs (C)
• V = potential difference across the plates, measured in volts (V)

What does 1 farad mean? A capacitance of 1 F means that 1 coulomb of charge is stored when the potential difference across the plates is 1 volt. In practice, 1 farad is an enormous value — most capacitors have capacitances measured in:

• μF (microfarads) = 10⁻⁶ F
• nF (nanofarads) = 10⁻⁹ F
• pF (picofarads) = 10⁻¹² F

Examiner tip: The letter "C" is used both for capacitance (a quantity) and as the unit coulombs (for charge). Be careful not to confuse them in calculations.

Key idea: A larger capacitance means the capacitor can store more charge for the same voltage. Think of it like a bucket — a bigger bucket (larger C) can hold more water (charge) at the same water level (voltage).