Question

Prove that the resistance of R₁, R₂ and R₃ in parallel is given by the expression:

R₁R₂R₃/(R₁R₂ + R₂R₃ + R₃R₁).

Answer 1

Equivalent resistance R is given by:

\(\frac 1R = \frac 1{R_1} + \frac 1{R_2} + \frac 1{R_3}\)

⇒ \(R = \frac {R_1 R_2R_3}{R_1R_2 + R_2R_3 + R_3R_1}\)