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A wire's diameter is doubled. What …

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A wire's diameter is doubled. What will be the new resistance?

  • 1 answers

Naveen Sharma 6 years, 10 months ago

Ans. 

We know that 

Resistance R = {tex}\rho {L\over A}{/tex}

Where {tex}\rho{/tex} is resistivity of material

L is length of wire

A is area of Cross-section of wire

Area A = {tex}\pi r^2{/tex}

If we double the Diameter it means radius is also doubled 

So now Area = {tex}\pi (2r)^2= 4\pi r^2{/tex} = 4A

So  New Resistance R' = {tex}\rho {L\over 4A} = {R\over 4}{/tex}

Means new resistance will be {tex}({1\over 4})^{th}{/tex} of old resistance .

 

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