A constantan wire of length $50 c m$ and $0.4 m m$ diameter is used in making a resistor. If the resistivity of constantan is $5 \times 10^{- 7} Ω - m$ , calculate the value of the resistance.

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Solution

Given,
length $l = 50 c m = 0.50 m$
resistivity $ρ = 5 \times 10^{- 7} Ω - m$
diameter $d = 0.4 m m$
$∴$ radius $r = 0.2 m m = 0.2 \times 10^{- 3} m$

Now,
Area $A = π r^{2}$
$A = π {(0.2 \times 10^{- 3})}^{2} m^{2}$

$R = \frac{ρ l}{A} = \frac{5 \times 10^{- 7} \times 0.5}{π \times 0.2 \times 0.2 \times 10^{- 6}}$

$R = 1.99 Ω$

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A constantan wire of length 50 cm and 0.4 mm diameter is used in making a resistor. If the resistivity of constantan is 5×10−7 Ω−m, calculate the value of the resistance.

Given,length l=50 cm=0.50 m resistivity ρ=5×10−7 Ω−mdiameter d=0.4 mm ∴ radius r=0.2 mm=0.2×10−3 mNow,Area A=πr2A=π(0.2×10−3)2 m2R=ρlA=5×10−7×0.5π×0.2×0.2×10−6R=1.99 Ω

A constantan wire of length $50 c m$ and $0.4 m m$ diameter is used in making a resistor. If the resistivity of constantan is $5 \times 10^{- 7} Ω - m$ , calculate the value of the resistance.