Question

You are given a resistance wire of length 50 cm and a battery of negligible resistance. In which of the following cases is the largest amount of heat generated?
(A) When the wire is connected to the battery directly.
(B) When the wire is divided into two parts and both the parts are connected to the battery in parallel.
(C) When the wire is divided into four parts and all the four parts are connected to the battery in parallel.
(D) When only half of the wire is connected to the battery.

Answer 1

Hint: This setup will work on the principle of Heating Effect of Electric Current. It occurs when the heat is produced by a conductor when the electric current stops flowing. This effect says that when an electric current is made to flow in a conductor, then heat energy is generated in the conductor.

Complete step by step answer:
Step I:
The heating effect of the current depends on three major factors. They are:
The amount of the current ‘I’ which flows through the conductor.
The resistance ‘R’ of the conductor.
The time ‘t’ for which the current flows in the conductor.
Formula for heating effect of current is \[H = {I^2}Rt\]
Step II:
There are four cases given. Since \[H \propto R\],
Case I: If connected directly, then resistance is R.
Case II: If the wire is divided into two equal parts, then resistance becomes \[\dfrac{R}{4}\].
Case III: If the wire is divided into four equal parts, then resistance becomes \[\dfrac{R}{{16}}\].
Case IV: If only half of the wire is connected then resistance is \[\dfrac{R}{2}\].
Step III:
For maximum heat to be generated, the resistance in the wire should also be maximum. A maximum amount of resistance is produced when the wire is divided into four equal parts.

$\therefore$ Option C is the right answer.

Note:
When resistance in the wire increases, the electrons gain energy and start moving at a fast speed to pass the conductor. As they move fast, there are more chances of collision between them. These collisions increase more energy in the form of heat. As a result the temperature of the conductor also increases.