Physics

Problem

Two identical, mutually perpendicular coils

A

and

B

are mounted on the same axis so that they rotate together in a uniform magnetic field with angular speed

\omega

. The coils are connected in series so that their individual emfs add algebraically. For coil

A

the induced emf is

e_A = e_0 \sin \omega t

. For coil

B

the initial orientation causes its emf to lead that of coil

A

90^{\circ}

. a. (i) Write the expression for the instantaneous emf

e_B

of coil

B

. b. (ii) Obtain an expression for the resultant instantaneous emf

e_{\text{res}}

produced by the series combination of the two coils. c. (iii) Show that the amplitude of

e_{\text{res}}

\sqrt{2}\,e_0

. Hence determine its root-mean-square (rms) value when

e_0 = 120\,\text{V}