The length of the manganese wire of the resistivity is 1 m is 1.84 x 10-6 32 m at 20 ° C. If the wire of the diameter is 3 x 10-4 m, what will be the temperature at the resistance of the wire?
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Given : The length of the manganese wire, l = 1m
resistivity of manganese wire, ρ = 1.84 × 10¯⁶ Ωm at 20°C.
diameter of wire, d = 3 × 10¯⁴ m
To find : resistance of wire at that temperature.
solution : using formula, R = ρl/A
here A = cross sectional area of wire
= πd²/4
= 3.14 × (3 × 10¯⁴)²/4
= 3.14 × 9/4 × 10^-8 m²
= 7.065 × 10^-8 m²
now Resistance of wire, R = (1.84 × 10¯⁶ Ωm × 1m)/(7.065 × 10^-8 m²)
= (1.84/7.065) × 10² Ω
= 0.26 × 10² Ω
= 26 Ω
Therefore the resistance of the wire at that temperature is 26 Ω.
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