An ideal inductor of inductance L is connected across an alternating voltage source. If the instantaneous voltage is given by V = V₀ ( t) , what is the expression for the instantaneous current I flowing through the circuit?

Step-by-step solution

In a purely inductive circuit, the current lags behind the voltage by a phase angle of 2 . Given the voltage V = V₀ ( t) , the phase of the current can be written as: I = I₀ ( t - 2 ) The peak current I₀ is related to the peak voltage V₀ by the inductive reactance X_L = L : I₀ = V₀ X_L = V₀ L Substituting I₀ into the current expression: I = V₀ L ( t - 2 ) Using the trigonometric identity ( - 2 ) = - ( ) , we get: I = - V₀ L ( t) Answer: - V₀ L ( t)