Electro Magnetic Induction And Alternating Currents Question 196

Question: In a uniform magnetic field of induction B a wire in the form of a semicircle of radius r rotates about the diameter of the circle with an angular frequency ω . The axis of rotation is perpendicular to the field. If the total resistance of the circuit is R, the mean power generated per period of rotation is

Options:

A) (Bπrω)22R

B) (Bπr2ω)28R

C) Bπr2ω2R

D) (Bπrω2)28R

Show Answer

Answer:

Correct Answer: B

Solution:

  • ϕ=B,.A, ;

    ϕ=BA,cos,ωt ε=dϕdt=ωBA,sin,ωt ;

    i=ωBAR,sin,ωt

    Pinst=i2R=(ωBAR)2×R,sin2,ωt

    Pavg=0TPinst×dt0Tdt=(ω,B,A)2R0Tsin2,ω,tdt0Tdt=12,(ω,B,A)2R
    Pavg=,(ω,B,π,r2)28,R

    [A=π,r22]



NCERT Chapter Video Solution

Dual Pane