Question

Calculate the ratio of the equivalent resistance of the above two wires in parallel combination to that in series combination.

Answer 1

The resistance of the two wires are R₁ = 2Ω and R₂ = 8Ω 

When they are connected in series.

Equivalent resistance = R₁ + R₂ 

⇒ R_eq = 2 + 8 = 10 Ω. 

R_eq in series = 10 Ω. 

When they are connected in parallel.

Equivalent resistance = \(\frac{1}{R_1}+\frac{1}{R_2}\)

⇒ \(\frac{1}{R_{eq}}=\frac{1}{2}+\frac{1}{8}\)

⇒ \(\frac{1}{R_{eq}}=\frac{4+1}{8}=\frac{5}{8}\)

⇒ \(\frac{1}{R_{eq}}=\frac{5}{8}\)

R_eq in Parallel = 8/5 Ω.

Ratio of Parallel to series = \(\frac{\frac{8}{5}}{10}=\frac8{50}=\frac4{25}\)

Hence the ratio of the Equivalent resistances in parallel to series is 4/25