A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be: (Assume the coil to be short circuited.)
- Halved
- Quadrupled
- The same
- Doubled
The Correct Option is D
Solution and Explanation
As number of turns are halved so length of wire is halved, and radius is doubled, then area will be 4 times the previous one if previous resistance is R then new resistance is R/8 and if previous emf is E then new emf will be E/2 so
Pi = \(\frac{E^2}{R}\)
Pf = \(\frac{(E/2)^2}{R/8} =\frac{2E^2}{R}=2P_i\)
As the answer key is changing students can challenge this question.
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Concepts Used:
Electric Power
Power is defined as the rate of doing work. Electric power is the rate at which electrical energy is transferred through an electric circuit, i.e. the rate of transfer of electricity. The symbol for Electric Power is ‘P’. SI unit of electric power is Watt.
Electric Power Formula
P = VI
From Ohm's Law, V = IR
Hence, Power can also be expressed as P = I2R