Answer

Verified

80.4k+ views

**Hint**The change in the length of the wire can be determined by using the joules law of heating formula, by using the relation which showed by the joules law of heating formula, the change in the length of the wire for the given condition is determined.

**Useful formula**

The joules law of heating is given by,

$H = \dfrac{{{V^2}t}}{R}$

Where, $H$ is the heat of the wire, $V$ is the potential difference in the wire, $t$ is the time taken and $R$ is the resistance.

**Complete step by step solution**

Given that,

The time taken by the electric kettle to boil is, $t = 10\,\min $,

The heating element is modified then the time taken is, $t = 7\,\min $.

Now,

The joules law of heating is given by,

$H = \dfrac{{{V^2}t}}{R}\,..............\left( 1 \right)$

In the above equation (1), the resistance of the wire is written as,

$H = \dfrac{{{V^2}t}}{{\left( {\dfrac{{\rho L}}{A}} \right)}}$

By rearranging the terms in the above equation, then the above equation is written as,

$H = \dfrac{{{V^2}tA}}{{\rho L}}$

In the question the relation is given as heat, time taken and the length. So that assume the other terms as constant, then the above equation is written as,

$H \propto \dfrac{t}{L}$

From the above equation, the heat is inversely proportional to the length of the wire. To increase the heat of the wire, then the length of the wire is decreased.

**Hence, the option (B) is the correct answer.**

**Note**The heat developed in the wire is directly proportional to the potential difference in the wire, time taken and the heat developed in the wire is inversely proportional to the resistance of the wire. As the potential difference in the wire, time taken increases, then the heat developed also increases.

Recently Updated Pages

Name the scale on which the destructive energy of an class 11 physics JEE_Main

Write an article on the need and importance of sports class 10 english JEE_Main

Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main

Choose the one which best expresses the meaning of class 9 english JEE_Main

What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main

A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main