Question

a conductor has a length of 2m and radius of 3mm.If the resistance is 100 ohm, Calculate the new resistance if the same material has,

a)length 6m and radius 6mm
b)length 1m and radius 1mm

Answer 1

Answer:

( a )  75 Ω

( b ) 450

Step-by-step explanation:

We have been  given by question

Conductor has length l = 2 m

Radius  r = 3 mm

Resistance is 100 ohm

Now ,

We know that ,

$R = \rho\dfrac{l}{A}\\\\100= \dfrac{\rho.2}{\dfrac{\pi}{4}\times 3\times 3\times 10^{-6}} \\\\\rho\ =1125\times \pi \times 10^{-6}$

Part ( a )

We have been given by question

conductor has length l = 6 m

Radius  r = 6 mm

$R = \rho\dfrac{l}{A}\\\\ R=\dfrac{ 1125 \times 6}{\pi}{4}\times 6\times 6\times 10^{-6}$

Resistance R =75 Ω

Part ( b )

Conductor has length l = 1 m

Radius  1 = 3 mm

$R = \rho\dfrac{l}{A}\\\\ R=\dfrac{ 1125 \times 1}{\pi \times 1\times 1 \times 10^{-6} }{\times 4}\times 10^{-6}$

New resistance 450 Ω