It's Cold, Double the Heat

A metallic cylindrical conductor is used to produce some heat by applying a constant voltage between it's two ends. It's cold, and you need to double the heat released. Which of the following is the most appropriate thing to be done?

The radius be doubled Both the length as well as the radius of the conductor be doubled The length be doubled Both the length as well as the radius of the conductor be halved

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Ronak Agarwal
Sep 27, 2014

Simple

Power = V 2 R \frac{{V}^{2}}{R}

Also R = ρ l A = ρ l π r 2 R=\frac{\rho l}{A}=\frac{\rho l}{\pi {r}^{2}}

Power = P = π r 2 V 2 ρ l P= \frac{\pi {r}^{2}{V}^{2}}{\rho l}

To double the heat you have to double the power hence simply double the radius as well as length because :

= π ( 2 r ) 2 V 2 ρ ( 2 l ) = 2 π r 2 V 2 ρ l = 2 P =\frac { \pi { (2r) }^{ 2 }{ V }^{ 2 } }{ \rho (2l) } =2\frac { \pi { r }^{ 2 }{ V }^{ 2 } }{ \rho l } =2P

I doubled resistance instead of power. Anyway it was a good question..

vivek sedani - 6 years, 8 months ago

Log in to reply

Thanks... @_@

Satvik Golechha - 6 years, 8 months ago

If I double only the radius,then I will get greater power

Arnav Agarwal - 4 years, 5 months ago

To increase the heat we have to increase current, to increase current have to reduce the resistance so by increasing area we can reduce the resistance so I think the ans is radius is doubled

Guna Sekar - 5 years, 2 months ago

Exactly. Thanks. This was my first E&M problem.

Satvik Golechha - 6 years, 8 months ago

Log in to reply

I see. So are you in 11th class or 10th class.

Ronak Agarwal - 6 years, 8 months ago

Log in to reply

10th. And you in 12th?

Satvik Golechha - 6 years, 8 months ago

Log in to reply

@Satvik Golechha Yes. Then you would have only basic knowledge of mechanics.

Ronak Agarwal - 6 years, 8 months ago

Log in to reply

@Ronak Agarwal @Ronak Agarwal what resources do you use for EM and Geometry

Mardokay Mosazghi - 6 years, 8 months ago

Log in to reply

@Mardokay Mosazghi Honestly speaking I am not very good in geometry, I am good only in analytical geometry, while preparing for IIT-JEE we do topics like Geometry of triangles, also we prepare a lot for co-ordinate geometry and trignometry which makes many of the good geometry problems possible to solve for me.

For Electricity and Magnetism I have only the resources given to me by coaching centre in which I am studying, for the preparation of IIT-JEE.

Ronak Agarwal - 6 years, 8 months ago

Log in to reply

@Ronak Agarwal thanks for the reply, you are a great inspiration to me solving every level 5 EM and Mechanics questions.

Mardokay Mosazghi - 6 years, 8 months ago

@Ronak Agarwal I know a little bit of class 11, like projectile and relative.

Satvik Golechha - 6 years, 8 months ago

Hey I'm also 14 . I would like to be your friend .. I'm too interested in phu and am in class 9 but completed all class 10 maths and physics .. Can you tell me which book is good yo read the advance phy ?

Avisek Agarwal - 6 years, 6 months ago

nice first problem

Mardokay Mosazghi - 6 years, 8 months ago

Log in to reply

Thanks... :D

Satvik Golechha - 6 years, 8 months ago

The second equation relating resistance and resistivity is wrong. The area, 'A' should be in the denominator. But you have substituted correctly in the third step, so the final result is correct

Ananthakrishnan AJ - 6 years, 8 months ago

Log in to reply

Sorry for the typo.

Ronak Agarwal - 6 years, 8 months ago

This question requires review. Remember the voltage is constant, doubling the radius reduces the resistivity hence reducing the heat production.

Kh Tang - 1 month, 3 weeks ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...