For four identical resistors in parallel, the effective resistance is: R/4 = 0.25 ⇒ R = 1Ω In series, total resistance is: R series= 4R = 4 × 1 = 4Ω Thus, the correct answer is (a) 4 Ω.
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Resistance of a wire is given by R = ρ L/A . When stretched, L ′ = 1.5L and = A/(1.5)², so new resistance: R ′ = ρ 1.5L/A/(1.5)² = 2.25R To make R′ = 4R, solving gives fraction 1/6. ...