(a) Define the term "phase difference" between the alternating voltage and the alternating current in an electrical circuit.
(b) Show that the time lag Δt between the instants when the voltage and current attain their corresponding positive maximum values is related to the phase difference ϕ and the angular frequency ω of the source by the relation Δt=ωϕ. State clearly the assumptions made, if any.
(c) An AC source operates at a frequency of 50Hz. If in a certain circuit the current is observed to lag behind the applied voltage by 30∘, calculate the numerical value of the time lag between their positive maxima.