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In a certain single-phase a.c. circuit the instantaneous voltage is given by v = V sin (ωt + 30°) p.u. and the instantaneous current is given by i = I sin (ωt - 30°) p.u. Hence the per unit value of reactive power is
  • a)
    1/4
  • b)
    1/2
  • c)
    √3/4
  • d)
    √3/2
Correct answer is option 'C'. Can you explain this answer?
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Ωt), where v is the instantaneous voltage, V is the maximum voltage amplitude, ω is the angular frequency, and t is the time.

The instantaneous current in this circuit can be given by i = I sin (ωt + φ), where i is the instantaneous current, I is the maximum current amplitude, and φ is the phase angle.

The power in this circuit can be calculated using the formula P = vi, where P is the power, v is the instantaneous voltage, and i is the instantaneous current.

Substituting the given equations for v and i, we get P = (V sin (ωt)) * (I sin (ωt + φ)).

Using the trigonometric identity sin(a) * sin(b) = 1/2 * (cos(a - b) - cos(a + b)), we can simplify the expression for power to:

P = (V * I / 2) * (cos(φ) - cos(2ωt + φ))

Therefore, the power in this single-phase a.c. circuit can be expressed as P = (V * I / 2) * (cos(φ) - cos(2ωt + φ)).
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In a certain single-phase a.c. circuit the instantaneous voltage is given by v = V sin (ωt + 30°) p.u. and the instantaneous current is given by i = I sin (ωt - 30°) p.u. Hence the per unit value of reactive power isa)1/4b)1/2c)√3/4d)√3/2Correct answer is option 'C'. Can you explain this answer?
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