In a circuit of figure, Vs = 10 cos(ωt) power drawn by the 2Ω resistor is 4 watts. The power factor is

Let I be the current, then P = I² R

I is the rms current.

⟹ P_rms = I² R ⟹ 4 ⟹ I² = 4 ⟹ I = 2A.

Total power drawn = V_m I_m cos θ

⟹ 10 x 2 cos θ = 10 cos θ

Total power cannot be determine until value of R = 12 Ω is given.