Worked example: In a Wheatstone bridge, P = 100 Ω, Q = 1000 Ω, and balance is achieved with R = 450 Ω from the resistance box. Find the unknown S. Also, if P and Q are swapped, what R balances? Step 1: Balance condition P/Q = R/S, so S = R·Q/P = 450 × 1000/100 = 4500 Ω = 4.5 kΩ. Step 2: The ratio arms P:Q = 1:10 multiply the box reading by 10 — this is how the bridge measures resistances far larger than the box contains. Step 3: Swapped: P = 1000, Q = 100, balance needs R/S = 1000/100 = 10, so R = 10 × 4500 = 45,000 Ω — beyond a typical box, showing why you choose the ratio arms to keep R in range. Practical tip: start with P = Q (1:1) for a rough value, then switch ratios for precision.