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NEETPhysicsAlternating Current

A purely capacitive circuit with capacitance C is connected to an ac source. If the alternating current flowing in the circuit is given by I = I₀ ( t) , the instantaneous voltage V_C across the capacitor is

Options

  1. AI₀ C ( t)
  2. BC I₀ ( t)
  3. C- C I₀ ( t)
  4. D- I₀ C ( t)

Correct answer

D. - I₀ C ( t)

Step-by-step solution

In a purely capacitive circuit, the voltage lags behind the current by a phase angle of 2 . Given the current I = I₀ ( t) , the voltage can be expressed as: V_C = V₀ ( t - 2 ) The peak voltage V₀ is related to the peak current I₀ by the capacitive reactance X_C = 1 C : V₀ = I₀ X_C = I₀ C Substituting V₀ into the voltage expression: V_C = I₀ C ( t - 2 ) Using the trigonometric identity ( - 2 ) = - ( ) , we get: V_C = - I₀ C ( t) Answer: - I₀ C ( t)

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