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

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=

⇒

⇒

⇒

R_eq in Parallel = 8/5 Ω.

Ratio of Parallel to series =

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