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

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

Vs = 10 cos ωt, Let I be the current, then P = I2 R I is the rms current. ⟹ Prms = I2 R ⟹ 4 ⟹ I2 = 4 ⟹ I = 2A. Total power drawn = Vm Im cos θ ⟹ 10 x 2 cos θ = 10 cos θ Total power cannot be determine until value of R = 12 Ω is given.

0.3
0.4
0.6
none

Correct Answer: 0.6

Explanation:

V_s = 10 cos ωt,

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.

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