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JEE MainPhysicsAlternating Current

An alternating current composed of two sinusoidal components with the same frequency flows through a resistor of resistance R . The current is given by I = I₀ t + I₀ ( t + 3 ) . The average power dissipated in the resistor is

Options

  1. AI₀^2 R
  2. B3 I₀^2 R
  3. C3 2 I₀^2 R
  4. D2 I₀^2 R

Correct answer

C. 3 2 I₀^2 R

Step-by-step solution

The given current is a superposition of two alternating currents with a phase difference of 3 (or 60^ ). Using phasor addition, the resultant peak current I_m is: I_m = I₀^2 + I₀^2 + 2 I₀ I₀ ( 3 ) Since ( 3 ) = 1 2 : I_m = 2 I₀^2 + 2 I₀^2 ( 1 2 ) = 3 I₀ The r.m.s. value of the resultant current is: I_ rms = I_m 2 = 3 2 I₀ The average power dissipated in the resistor R is: P = I_ rms ^2 R = ( 3 2 I₀ )^2 R = 3 2 I₀^2 R Answer: 3 2 I₀^2 R

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