A wire of length 10 cm and radius 7 × 10⁻⁴ m connected across the right gap of a meter bridge. When a resistance of 4.5 Ω is connected on the left gap by using a resistance box, the balance length is found to be at 60 cm from the left end. If the resistivity of the wire is R × 10⁻⁷ Ωm, then value of R is :
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Question

A wire of length 10 cm and radius 7 × 10⁻⁴ m connected across the right gap of a meter bridge. When a resistance of 4.5 Ω is connected on the left gap by using a resistance box, the balance length is found to be at 60 cm from the left end. If the resistivity of the wire is R × 10⁻⁷ Ωm, then value of R is :

Options

G1 Physics · Accepted Answer

For the meter bridge at balance, 4.5/Rw = 60/40 Therefore, Rw = 3 Ω Also, Rw = ρl/(πr²) 3 = ρ(0.1) / [π(7 × 10⁻⁴)²] Thus, ρ ≈ 66 × 10⁻⁷ Ωm Hence, R = 66 Correct option: C.