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KCET2016PhysicsAlternating Current

In a series L.C.R. circuit an alternating emf (v) and current (i) are given by the equation ( v=v₀ t, l=i₀ ( t+ 3 ) ) The average power discipated in the circuit over a cycle of ( A C ) is

Options

  1. A( v₀ i₀ 2 )
  2. B( v₀ i₀ 4 )
  3. C( 3 2 v₀ i₀ )
  4. DZero

Correct answer

B. ( v₀ i₀ 4 )

Step-by-step solution

Given, emf ( v=v₀ t ; ) current ( i=i₀ ( t+ 3 ) ) Then, average power dissipated in circuit over a cycle of ac is ( P_ avg =v_ rms i_ ms ) We know, ( v_ ms = v₀ 2 ; i_ rms = i₀ 2 ; = 3 ) ( P_ avg = v₀ 2 i₀ 2 ( 3 )= v₀ i₀ 2 1 2 = v₀ i₀ 4 ) ( P_ avg = v₀ 2 i₀ 2 ( 3 )= v₀ i₀ 2 1 2 ) Thus, average power dissipated ( = v₀ i₀ 4 )

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