An alternating current given by I = I₀ t flows through a purely inductive circuit of inductance L . Which of the following expressions represents the instantaneous power P supplied to the inductor by the source?

Step-by-step solution

The voltage across a pure inductor is given by V = L dI dt . Given I = I₀ t , we have: V = L d dt (I₀ t) = L I₀ t The instantaneous power P is the product of instantaneous voltage and current: P = V I = ( L I₀ t)(I₀ t) Using the trigonometric identity 2 = 2 , we get: P = 1 2 L I₀^2 (2 t t) = 1 2 L I₀^2 2 t Note that while the average power over a complete cycle is zero, the instantaneous power varies sinusoidally with twice the frequency of the source. Answer: 1 2 L I₀^2 2 t