Day 37 · Feb 6

Birthday of Charles Wheatstone (1802) — The Bridge of Resistance

Charles Wheatstone was born on February 6, 1802. Though Samuel Christie invented the circuit in 1833, it is Wheatstone who popularised and perfected what became known as the Wheatstone bridge: four resistors arranged in a diamond, with a galvanometer across the middle. When the bridge is 'balanced' — the ratio of two pairs of resistors is equal — no current flows through the galvanometer. This balance condition R₁/R₂ = R₃/R₄ allows unknown resistance to be measured with extraordinary precision. The mathematics is a direct application of Kirchhoff's laws: the sum of currents at any node is zero; the sum of voltages around any loop is zero.

In a Wheatstone bridge, three resistors are known and one is unknown. Derive the formula for the unknown resistance when the bridge is balanced.

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