12: Electromagnetic Induction. 12.2 Alternating Current. Alternating Current Demo: HEP demo or dynamo Alternating Current and Voltage
12.2 Alternating Current
Demo: HEP demo or dynamo
Alternating Current and Voltage
Whenever a magnet rotates near a coil or wire, its flux will move through the wire or coil inducing an alternating EMF across the coil or wire as a result of Faraday’s Law.
A very simple AC generator can consist of a single coil of copper wire being forced to rotate in a uniform magnetic field as shown. At the each end of the wire are connected circular ‘slip rings’.
Q1.Explain the design and purpose of the ‘slip rings’
Q2.Why is the coil made from copper wire?
Link: AC Generator Applet
This simplified diagram shows a coil ‘end-on’, rotating anti-clockwise:
Q3.Explain using Faraday’s Law why the EMF will vary from maximum to zero as angle θ (between the normal to the coil and the field plane) goes from 90° to zero (as shown in the diagrams).
Q4. anti-clockwise:Plot points on the graph of flux linkage against time (for max positive flux linkage, max negative, zero) and draw the line that goes through them. Considering Faraday’s Law, similarly plot points on the graph of EMF against time and draw the line.
As can be seen from the two graphs, if EMF (ε) is a sinusoidal graph then flux linkage must give a cosine graph.
In fact the equations for each are...
Nϕ = BAN cosθ(or Nϕ = BAN cosωt)
ε = BAN ω sin θ (or ε = BAN ω sin ωt)
(You do not need to know these equations however they should make sense to you).
Root Mean Square Current sinusoidal graph then flux linkage must give a cosine graph.
In mathematics the Root Mean Square (rms) is a statistical method of determining the magnitude of a quantity that is varying. It can be thought of as a kind of ‘average’ value. In particular it is useful when dealing with sinusoidal variations (that can be positive or negative) such as induced EMF and current from a rotating coil.
For discrete values of any quantity the following formula can be applied:
Clearly the calculated value is the square root of the mean of the squares of the discrete values.
Q6.Determine the rms value of current from the following graph using eight successive discrete values:
For electrical output from a coil rotating at constant speed in a uniform magnetic field, the following formulae can be applied:
εrms = ε0
ε0= Maximum EMF (V)
I0 = Maximum current (A)
Irms = I0
Power in AC circuits in a uniform magnetic field, the following formulae can be applied:
When calculating the power dissipated in an AC circuit, we use the rms values.
Thus, for alternating current circuits...
The rms value of an alternating current is identical to the value of direct current that would dissipate power at the same rate through a resistor.
Power = Irms x Vrms
Primary coil in a uniform magnetic field, the following formulae can be applied:
If any two electrical circuits are near to each other, a changing current in one can cause an induced EMF in the other.
A transformer uses changing flux linkage produced by one coil to induce an EMF in the second coil.
The input current is in a uniform magnetic field, the following formulae can be applied:a.c.
Plot a graph of current in the primary (Ip) against time.
The flux in the core is proportional to Ip.
Plot a graph of flux in the core against time.
The EMF induced in the secondary is proportional to the rate of change of flux linkage.
Plot a graph of Induced EMF in the secondary against time.
V in a uniform magnetic field, the following formulae can be applied:sNs
The flux passing through the primary and secondary coils is identical in a 100% efficient transformer.
Q.Explain (using Faraday’s Law) why having more turns in the secondary than the primary can lead to the voltage being ‘stepped up’ (increased).
The ratio of the turns is equal to the ratio of the voltages:
Ideal Transformers in a uniform magnetic field, the following formulae can be applied:
A 100% efficient transformer is known as an ‘ideal transformer’. In this case all the power on the primary side is transferred to the secondary side.
(All values are rms values)
IpVp = IsVs
Q. in a uniform magnetic field, the following formulae can be applied:If Np < Ns, which of the following are true (re-write the wrong statements):
a. ϕp = ϕs
b. flux linkage is equal in both coils
c. Ip > Is
d. Vp > Vs