Derive the formula for the equivalent resistance of three resistors joined in parallel. Find the equivalent resistance of 10 Ω, 20 Ω and 20 Ω joined in parallel.

1. 1 · Draw the circuit. [Sketch: R₁, R₂, R₃ as three branches between P and Q; cell, key and ammeter in the main line]
2. 2 · Same p.d. across each. Each resistor is joined across P and Q, so each has the same p.d. V.
3. 3 · Currents add up. i = i₁ + i₂ + i₃, where i₁ = V/R₁, i₂ = V/R₂, i₃ = V/R₃.
4. 4 · Use the equivalent resistance. i = V/Rp, so V/Rp = V/R₁ + V/R₂ + V/R₃.
5. 5 · Get the result. Divide by V: 1/Rp = 1/R₁ + 1/R₂ + 1/R₃.
6. 6 · Substitute the values. 1/Rp = 1/10 + 1/20 + 1/20 = 2/20 + 1/20 + 1/20 = 4/20.
7. 7 · Answer. Rp = 20/4 = 5 Ω, which is smaller than the smallest resistor (10 Ω).

Scoring tip: Turn the fraction over at the end. Many learners stop at 1/Rp = 4/20 and lose the last mark.