Question

derive expression for
Average power in ac circuit

Answer 1

An expression for  Average power in ac circuit

• we know that, equation for power is given by,
• P = VI
• let, I = Im sin(wt + Ф) and V = Vm sin wt
• ∴ P =  Vm sin wt × Im sin(wt + Ф)
• = Vm Im × sin wt × sin(wt + Ф)
• = VmIm/2 × 2sin wt × sin(wt + Ф)
• = VmIm/2 [ cos (wt - wt + Ф) - cos (2wt + Ф) ]
• = VmIm/2 [ cos Ф - cos (2wt + Ф) ]
• here cos (2wt + Ф) = 0, as this term is dependent on time
• = VmIm/2 [ cos Ф ]
• ⇒ P = VI cos Ф
• as for ac circuit, we have, V = IZ
• ∴ P = I^2Z cos Ф    is the required expression