Graphical representation of charging and discharging of capacitors through…

The idea

When a capacitor charges through a resistor, the current is initially large because the p.d. across the capacitor is zero, so the full supply p.d. appears across the resistor. As charge builds, the capacitor p.d. rises and the current falls, so the charging curve is steep at first and flattens towards the supply value. Discharging reverses the process: the capacitor drives current through the resistor, and both charge and current decay towards zero. The shape is exponential, with a constant time constant τ = RC. A useful method is to plot the variable against time, identify the initial value and the asymptote, then check that the curve falls to about 37% of its starting value after one time constant.

What earns the marks

• Charging curves for charge and p.d. rise from zero and approach the supply value asymptotically, never overshooting it.
• Discharging curves for charge and p.d. fall from their initial values towards zero asymptotically.
• Charging current starts at a maximum value equal to supply p.d. divided by resistance and decays towards zero.
• Discharging current starts at a maximum value equal to initial capacitor p.d. divided by resistance and decays towards zero.
• The time constant τ = RC determines the rate: a larger resistance or capacitance gives a slower approach to the final value.
• After one time constant, a discharging quantity has fallen to about 37% of its initial value, and a charging quantity has reached about 63% of its final value.

Common mistakes and how to put them right

• Drawing charging and discharging curves as straight lines.

  Put it right: The correct curves are exponential, with a changing gradient.

• Showing the charging p.d. curve passing above the supply p.d.

  Put it right: The correct curve approaches the supply p.d. asymptotically from below.

• Confusing the current and p.d. curves during charging.

  Put it right: The correct current curve starts high and decays, while the p.d. curve starts at zero and rises.

Exam tips

• Label the axes with the quantity and unit, and mark the initial value and the asymptote before sketching the curve.
• Use the time constant to justify the shape: state that after one τ the value is about 37% or 63% of the way to its final value.
• When comparing two circuits, refer to the product RC rather than only to R or C separately.