The number of turns in the coil of an $AC$ generator are $50$ and its cross-sectional area is $2.5 \ m^2$. This coil is revolving in a uniform magnetic field of strength $0.3 \ T$ with a uniform angular velocity of $60 \ rad \ s^{-1}$. The resistance of the circuit comprising the coil is $500 \ \Omega$. The maximum induced $emf$ and maximum current produced in the generator are:

  • A
    $2.25 \ kV, 4.5 \ A$
  • B
    $2.25 \ kV, 2.5 \ A$
  • C
    $4.5 \ kV, 4.5 \ A$
  • D
    $3.25 \ kV, 2.5 \ A$

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Write down the formula for the induced $emf$ in an $AC$ generator and discuss how it varies with time.

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