KinexiaLEARN PHYSICS

Capacitance — Keyboard Key (Worked Example)

Medium
Problem

Each key of a capacitive keyboard is a 10 pF capacitor charged to 5.0 V. How much charge sits on a key?

Given

  • C = 10 pF = 1.0 × 10⁻¹¹ F

  • V = 5.0 V

Find

The charge Q.

Principle

Even picofarad capacitors obey Q = CV — the keyboard detects your press by sensing this tiny charge shift.

Formula

Solution

  1. Convert: C=1.0×10−11 FC = 1.0 \times 10^{-11}\ \mathrm{F}

  2. Substitute: Q=(1.0×10−11)(5.0)Q = (1.0 \times 10^{-11})(5.0)

  3. Multiply: Q=5.0×10−11 CQ = 5.0 \times 10^{-11}\ \mathrm{C}

5.0 × 10⁻¹¹ C

Unit check

F × V = C — correct.

What this means physically

50 picocoulombs — an absurdly small charge, yet the keyboard's chip detects its change reliably millions of times. Modern electronics routinely sense single femtocoulombs.

Common mistake

Writing 10 pF as 10⁻⁹ F. Pico is 10⁻¹², nano is 10⁻⁹ — one letter, a factor of 1000.