An alternating voltage given by the equation V = V₀ (100 t) is applied across a purely inductive circuit. What is the minimum time after t = 0 that the current in the circuit reaches its maximum positive value?

Step-by-step solution

In a purely inductive circuit, the current lags the voltage by a phase angle of 2 radians. Given the voltage equation V = V₀ (100 t) , the current equation can be written as: I = I₀ (100 t - 2 ) = -I₀ (100 t) For the current to reach its maximum positive value ( I = I₀ ), we must have: -I₀ (100 t) = I₀ (100 t) = -1 The smallest positive angle for which the cosine is -1 is . Therefore, 100 t = t = 1 100 s. Answer: 1 100 s