Question

20) In a model AC generator a 502 turn rectangular coil 8.0 cm by 20cm rotates at 123 rev / min in a uniform magnetic field of 0.62 T

(a) what is the maximum emf induced in the coil?

(b) what is theinstantaneous value of the emf in the coil at t = (? / 32) s? assume that the emf is zero at t = 0 s?

(c) what is the smallest value of t for which the emf will have the its maximum value?

Answer 1

Given
No of turns N = 502
area of the rectangular coil A =8*20cm2
= 160cm2
= 160*10-4m2
angular frequency ? = 123rev/min
= 123*2?/60 rad/s
magnetic field B = 0.62 T
a)
The maximum emf is ?max = NBA?
= 64.14 V

b)
at t = (?/32) sthe instantaneous value of the emf in the coil is
? =?maxsin?t

= 61.16 V
c)
? = NBA?sin?t
? is maximum when sin?t = 1
or sin?t = sin?/2
or ?t = ?/2
so t =?/2?

= 5/41 or 0.122 s

Answer 2

Answer 3

The induced emf is given as follow

?= NBAw sin wt    or    ? = ?(max)sin?t

N - number of turns = 502 turns

B - magnetic field induction = 0.62 T

A

Answer 4

a) emf_max = N*A*B*w

= 502*8*20*10^-4*0.62*12.874

= 64.11 volts <<<<<<<<<<<<<<------------------------Answer

b)

emf = N*A*B*w*sin(w*t)

at t = pi/32 s

= 64.11*sin(12.874*pi/32)

= 61.11 volts <<<<<<<<<<<<<<------------------------Answer

c)when emf is maximum

sin(w*t) = 1

==> sin(w*t) = sin(pi/2)

==> t = pi/(2*w)

= 3.14/(2*12.874)

= 0.122 s <<<<<<<<<<<<<<------------------------Answer