Question

In a series L.C.R. circuit an alternating emf (v) and current (i) are given by the equation v= v₀ sinωt, i = i0 sin (ωt +π/3) The average power dissipated in the circuit over a cycle of AC is

(1) v₀i₀/4
(2) zero
(3) v₀i₀/2
(4) √3/2 v₀ i₀

Answer 1

The average power dissipated in the circuit over a cycle of AC in a series RLC circuit can be calculated using the formula Pave = Irms Vrms cos φ. In this case, the average power is (v0 * i0)/2, corresponding to option (3).

Step-by-step explanation:

The average power dissipated in a series RLC circuit can be calculated using the formula:

Pave = Irms Vrms cos φ

Where Irms is the rms value of the current, Vrms is the rms value of the voltage, and φ is the phase angle between the voltage and current.

In this case, the current (i) is given by i = i0 sin(ωt + π/3) and the voltage (v) is given by v = v0 sin(ωt). From these equations, we can determine that the phase difference between the voltage and current is π/3.

Since the power factor cos(π/3) = 1/2, the formula for average power simplifies to:

Pave = (i0 * v0)/2

Therefore, the average power dissipated in the circuit over a cycle of AC is (v0 * i0)/2, which corresponds to option (3).