The capacitor and the resistor-capacitor (RC) network: how a capacitor charges and discharges through a resistor, the shape of the voltage-time curves, and how the RC combination produces a time delay.

What this topic is asking

WJEC Eduqas wants you to understand the capacitor and the resistor-capacitor (RC) network: how a capacitor charges and discharges through a resistor, the shape of the voltage-time curves, and how the RC combination is used to make a time delay. This is the basis of the 555 timer circuits that follow.

The capacitor

A capacitor is like a tiny rechargeable store: pushing charge in raises its voltage, and letting charge out lowers it. Once fully charged from a steady supply, no more current flows into it, so it blocks steady DC. The useful behaviour for timing is what happens while it is charging or discharging, which takes time set by the resistor in series with it.

Charging through a resistor

At the instant charging begins, the capacitor is empty, so the full supply voltage is across the resistor and a large current flows, charging it quickly. As the capacitor voltage rises, less voltage is left across the resistor ($V_R = V_{\text{supply}} - V_C$), so the current falls and charging slows. The voltage therefore approaches the supply along a flattening curve, never quite reaching it. This rising, flattening shape is the charging curve you must be able to sketch.

Discharging through a resistor

Discharging is the mirror of charging: the capacitor drives a current through the resistor, and as its voltage falls the current falls too, so the voltage decays towards zero along a flattening curve. The same RC combination sets how fast this happens. Both the charging and discharging curves have the same characteristic shape, just rising or falling.

RC time delay

This is the key idea for timing circuits. A large resistor limits the current, so charging takes longer; a large capacitor needs more charge, so it also takes longer. Because the delay depends on the product $RC$, doubling either the resistor or the capacitor doubles the time. Designers pick $R$ and $C$ to give the delay they want - for example, the few seconds before a courtesy light fades. The 555 timer uses exactly this RC charging to set its timing.

Try this

Q1. State what happens to the charging current as a capacitor charges through a resistor. [1 mark]

• Cue. It is largest at the start and falls towards zero as the capacitor voltage rises.

Q2. State two ways to make an RC network charge more slowly. [2 marks]

• Cue. Use a larger resistor, or a larger capacitor (a larger $RC$ product).