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NEET2017PhysicsCurrent ElectricityActual

You are given resistance wire of length 50 cm and a battery of negligible resistance. In which of the following cases is largest amount of heat generated?

Options

  1. AWhen the wire is connected to the battery directly
  2. BWhen the wire is divided into two parts and both the parts are connected to the battery in parallel.
  3. CWhen the wire is divided into four parts and all the four parts are connected to the battery in parallel.
  4. DWhen only half of the wire is connected to the battery.

Correct answer

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

Step-by-step solution

Let R be the resistance of the wire (a) H₁= V^2 t R (b) Resistance of each part will be R / 2. When they are connected in parallel, the resistance will be R / 4 . Hence, H₂= 4 v^2 t R (c) In case of four wires connected in parallel, the resistance will be R / 8 H₃= 8 V^2 t R (d) H₄= V^2 t [R / 2] = 2 V^2 t R Hence, largest amount of heat will be generated in case of four parts connected in parallel.

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