Question

A fuse wire with a circular cross-section and having a diameter of 1 mm blows with a current of 3 ampere . the value of current for which another fuse wire made of the same material but having circular cross-section with diameter of 2 mm blow is ???

Answer 1

$\underline{\boxed{ \huge\purple{ \rm{Answer}}}}$

Given :

Radius of first wire = 1mm

Current blow in first wire = 3A

Radius of second wire = 2mm

To Find :

Current blow in second wire = ?

Concept :

Here both wire has same lenght and made up from same material therefore resistivity of both wires is also same...

Formula :

As per ohm's law V=IR

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We know that $\underline{\bold{\rm{R=\frac{\rho\:l}{A}}}}$

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Calculation :

$\implies \rm \: V = I \times \frac{ \rho \times l}{A} \\ \\ \therefore \rm \: \red{I \propto \: A} \\ \\ \implies \rm \: \frac{I_1}{I_2} = \frac{A_1}{A_2} = \frac{ {R_1}^{2} }{ {R_2}^{2} } \\ \\ \implies \rm \: \frac{3}{I_2} = { \frac{1}{2} }^{2} = \frac{1}{4} \\ \\ \therefore \underline{ \boxed{ \bold{ \rm{ \orange{I_2 = 12 \: A }}}}}$