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JEE MainPhysicsAlternating Current

A standard household alternating voltage supply has an RMS voltage of 220 ~V and a frequency of 50 ~Hz . Which of the following equations correctly represents the instantaneous voltage V(t) ?

Options

  1. AV = 220 2 (100 t)
  2. BV = 220 (100 t)
  3. CV = 220 2 (50 t)
  4. DV = 110 2 (100 t)

Correct answer

A. V = 220 2 (100 t)

Step-by-step solution

The peak voltage V₀ is related to the RMS voltage V_ rms by the relation: V₀ = V_ rms 2 = 220 2 ~V The angular frequency is related to the linear frequency f by the relation: = 2 f = 2 50 = 100 ~rad/s The standard equation for instantaneous alternating voltage is: V(t) = V₀ ( t) Substituting the values, we get: V(t) = 220 2 (100 t) Answer: V = 220 2 (100 t)

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