The armature of an ac generator is a coil of radius 5.70 cm and 120 turns. The c
ID: 1449525 • Letter: T
Question
The armature of an ac generator is a coil of radius 5.70 cm and 120 turns. The coil rotates in a uniform magnetic field with frequency 60.0 Hz. What is the strength of the magnetic field if the amplitude of the induced emf in the coil is 125.0 V? The primary coil of a transformer has 150 turns, while the secondary coil consists of 600 turns. What emf amplitude must be applied across the primary in order to get an emf of amplitude 320 V out of the secondary? A dc motor is connected to a battery with an emf of 6.00 V. The coil in the motor has a resistance of 0.850 Ohm, and produces a back emf of 3.50 V at normal operating speed. Find the current that flows through the motor when at its normal speed. A horizontal desk surface measures 70.0 cm by 145 cm. Find the magnetic flux through the desk surface due to a uniform magnetic field of magnitude 0.170 T, directed at an angle of 48.0degree below the horizontal.Explanation / Answer
Hi,
a) The value of the emf induced in the coil is equal to:
emf = NAB(2f) ; where N is the number of turns, A is the area of the a turn of the coil, B is the magnetic field and f is the frequency.
In this case we are assuming that the value of emf given is the maximum value reached by the coil.
The value of the area is equal to *r2 = *(5.7*10-2 m)2 = 0.0102 m2
B = emf / (2fNA) = 125 V / (2*60 Hz*120*0.0102 m2) = 0.271 T
b) The relation between the voltage of the primary and the secondary coil is given by:
m = Np / Ns = 150/600 = 0.25
Said relation then can be used then to find the primary voltage given the secondary one.
m = Vp / Vs :::::: Vp = mVs = (0.25)*320 V = 80 V
c) The current that flows through the motor at normal speed can be calculated as:
I = (emf - b.emf) / R ; where emf is the emf produced by the battery, b.emf is the back emf, R is the resistance through the motor and I is the current
I = (6.00 - 3.50) / 0.850 = 2.94 A
d) The magnetic flux through any surface can be calculated as:
F = BA cos () ; F is the magnetic flux, B is the magnetic field, A is the area and is the angle between the magnetic field vector and a vector normal to the area.
F = (0.170 T)*(70*10-2 m)*(145*10-2 m) cos (90° + 48°) = - 0.128 T
I hope it helps.
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