You are given 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?

When the wire is connected to the battery directly

When the wire is divided into two parts and both the parts are connected to the battery in parallel.

When the wire is divided into four parts and all the four parts are connected to the battery in parallel.

When only half of the wire is connected to the battery

Solution

When the wire is divided into four parts and all the four parts are connected to the battery in parallel.

Let R be the resistance of the wire

$H_{1} = \frac{V^{2} t}{R}$

b) The resistance of each part will be R/2. When they are connected in parallel, the resistance will be R/4.

Hence, $H_{3} = \frac{8 V^{2} t}{R}$ d)

d) $H_{4} = \frac{V^{2} t}{[R / 2]} = \frac{2 V^{2} . t}{R}$

Hence, the largest amount of heat will be generated in the case of four parts connected in parallel.

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