Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

A copper wire has diameter $0.5 mm$ and resistivity ρ = $1.6 \times 10^{- 8} ohm .$ What will be the length of its wire to make its resistance 10 ohm. In what ratio will the resistance change if diameter gets doubled?

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

100 m

1 : 4

122.66 m

1 : 2

122.66 m

1 : 4

None of these

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

A copper wire has diameter

0.5 mm

and resistivity ρ =

1.6 \times 10^{- 8} ohm .

The length of its wire should be

122.66 m

to make its resistance

10 ohm

. If diameter gets doubled, the resistance becomes

1 : 4 .

Radius = \frac{diameter}{2}

= \frac{0.5}{2}

= 0.25 mm

= 0.25 \times 10^{- 3} m

Resistivity ρ =

1.6 \times 10^{- 8} oh m^{- 1}

and

R = 10 ohm

We know that, resistance R =

\frac{ρl}{A}

10 = \frac{1.6 \times 10^{- 8} \times l}{π {(0.25 \times 10^{- 3})}^{2}}

Length l = 122.66 m

As we know, diameter

d = 2 r

. So,

r = d / 2

. Then,

{A = π d}^{2} / 4

If we double the diameter, then resistance will become one fourth.
Substituting this in the resistance formula, we get the ratio of resistances as

1 : 4 .

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Get Expert Academic Guidance – Connect with a Counselor Today!