4.5.2 The a.c. generator (3)
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1.
Question 2
The e.m.f. produced by an AC generator is plotted with time in the graph below.
a) What is the period of the AC e.m.f.?
b) What is the frequency of the AC e.m.f.?
c) Describe how the position of the generator coil relative to the magnetic field affects the shape of the e.m.f. graph.
a) The period of the AC e.m.f. is 2 seconds. This is the time taken for one complete cycle of the waveform.
b) The frequency of the AC e.m.f. is 1/2 Hz. Frequency is the reciprocal of the period (f = 1/T). Therefore, f = 1/2 s-1.
c) The position of the generator coil relative to the magnetic field directly affects the magnitude of the induced e.m.f. When the coil is aligned with the magnetic field, the e.m.f. is at its maximum. When the coil is perpendicular to the magnetic field, the e.m.f. is zero. As the coil rotates, the e.m.f. varies sinusoidally, reflecting the changing area of the loop exposed to the magnetic field. A larger number of turns in the coil will result in a larger e.m.f. for the same magnetic field and rotation speed.
2.
Question 2
A student builds a simple a.c. generator using a coil of wire and permanent magnets. They observe that the current produced is very low. Suggest two improvements the student could make to increase the amount of current produced. Explain the reasoning behind each suggestion, relating it to the principles of electromagnetic induction.
Here are two suggestions to increase the current produced by the a.c. generator, along with the reasoning:
- Increase the number of turns in the coil. The induced EMF in a coil is directly proportional to the number of turns of wire (EMF ∝ N). More turns mean a larger induced voltage, which in turn leads to a higher current if the resistance of the circuit remains constant. This is because a larger voltage drives more current through the circuit (Ohm's Law: I = V/R).
- Increase the speed of rotation of the coil. The frequency of the induced EMF is directly proportional to the speed of rotation (f ∝ ω). A faster rotation means the magnetic flux linking the coil changes more rapidly, resulting in a higher induced voltage and therefore a higher current. This is because a faster change in magnetic flux induces a larger EMF.
3.
Question 1
A simple AC generator consists of a coil of wire rotating within a magnetic field. A sketch graph of the e.m.f. produced by the generator with time is shown below.
a) Identify the type of e.m.f. that is produced by the generator.
b) Explain, in terms of the position of the generator coil within the magnetic field, how the e.m.f. changes with time.
c) State the value of the e.m.f. at the zero crossings.
a) The e.m.f. produced by the generator is alternating (AC) e.m.f.
b) As the coil rotates, the area of the loop exposed to the magnetic field changes. When the coil is aligned with the magnetic field, the induced e.m.f. is at its maximum. As the coil rotates away from the magnetic field, the induced e.m.f. decreases to zero when the coil is no longer aligned. The e.m.f. then increases again as the coil rotates back towards the magnetic field. This cyclical change in the area exposed to the magnetic field causes the e.m.f. to vary sinusoidally with time.
c) The e.m.f. at the zero crossings is zero volts. This is because the area of the loop is zero when the coil is aligned with the magnetic field, resulting in no induced e.m.f.