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Physics

Grade-9

Easy

Question

A 10 Ω resistor is to be made from manganin wire with a cross-sectional area of 0.2 mm². If manganin has a resistivity of 48 ×10^-8 Ohm-m, then the required length of this size manganin wire will be:

4.16 m
41.6 m
6.25 m
62.5 m

hint Hint:

R = $rho$ $l over A$

The correct answer is: 4.16 m

$R equals 10 space capital omega A equals 0.2 m m squared equals 0.2 cross times 10 to the power of negative 6 end exponent m squared rho equals 48 cross times 10 to the power of negative 8 end exponent capital omega m l equals ? R equals fraction numerator rho l over denominator A end fraction 10 equals fraction numerator 48 cross times 10 to the power of negative 8 end exponent cross times l over denominator 0.2 cross times 10 to the power of negative 6 end exponent end fraction rightwards double arrow l equals fraction numerator 10 cross times 0.2 cross times 10 to the power of negative 6 end exponent over denominator 48 cross times 10 to the power of negative 8 end exponent end fraction equals 0.0416 cross times 10 squared m equals 4.16 space m$

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