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The circuit shown in the figure consists of two resistances R 1 & R 2 connected to two ideal voltmetres V 1 & V 2 . Assume that a voltmeter reads ∆ V = - ∫ a b E → . d l → between its terminals. A time-varying magnetic field B ( t ) = B 0 t (where B 0 is a positive constant of proper dimensions and t is time) exists in a circular region of radius a and it is directed into the plane of the figure. The reading of voltm

Options

  1. Aπ a 2 B 0 R 1 R 1 + R 2
  2. B- π a 2 B 0 R 2 R 1 + R 2
  3. C- π a 2 B 0 R 1 R 1 + R 2
  4. Dπ a 2 B 0 R 2 R 1 + R 2

Correct answer

B. - π a 2 B 0 R 2 R 1 + R 2

Step-by-step solution

ϕ = π a 2 B 0 t ε = - d ϕ d t ⇒ ε = π a 2 B 0 (indeed emf) i = π a 2 B 0 R 1 + R 2 (induced current) ∆ V 1 = - ∫ a b E → . d l → = - - i R 1 = π a 2 B 0 R 1 R 1 + R 2 ∆ V 2 = - ∫ a b E → . d l → = - - i R 2 = - π a 2 B 0 R 2 R 1 + R 2

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