Question

A constant voltage is maintained between the two ends of a uniform metallic wire. As a result some heat is developed in it in time $t$. The heat developed in the same time is doubled if the original length $\left(l\right)$ and the radius $\left(r\right)$ of the wire are made equal to ______.

• A. $\frac{1}{2}$ and $\frac{r}{2}$
• B. $2l$ and $2r$
• C. $2l$ and $\frac{r}{2}$
• D. $\frac{l}{2}$ and $2r$

Answer 1

The correct option is B $2l$ and $2r$

Heat developed $=\frac{V^2}{R}t$ (1)

$R=p\frac{l}{A}$ where,

R=resistance, l= length and A=Area=$\pi r^2$

Heat developed will be doubled when resistance get halved

(Voltage = constant)

Resistance will get when length get doubled and radius also get doubled.

So length should become =2l

Radius should become = 2r