47 alternating current

7/31/2019 47 Alternating Current

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12: Electromagnetic

Induction12.2 Alternating Current


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Alternating Current

Demo: HEP demo or dynamo

Alternating Current and Voltage Whenever a magnet rotates near a coil or wire, itsflux will move through the wire or coil inducing analternating EMF across the coil or wire as a result ofFaradays Law.


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Rotating Coil in a Uniform Magnetic Field A very simple AC generator can consist of a single

coil of copper wire being forced to rotate in auniform magnetic field as shown. At the each endof the wire are connected circular slip rings.

Q1. Explain thedesign andpurpose of theslip rings

Q2. Why is thecoil made fromcopper wire?

Link: AC Generator Applet
http://www.fed.cuhk.edu.hk/sci_lab/Simulations/phe/generator_e.htmhttp://www.fed.cuhk.edu.hk/sci_lab/Simulations/phe/generator_e.htm


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This simplified diagram shows a coil end -on,rotating anti-clockwise:

Q3. Explain using Faradays Law why the EMF willvary from maximum to zero as angle (between thenormal to the coil and the field plane) goes from 90to zero (as shown in the diagrams).


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Q4. Plot points on the graph of flux linkage againsttime (for max positive flux linkage, max negative,

zero) and draw the line that goes through them.Considering Faradays Law, similarly plot points onthe graph of EMF against time and draw the line.


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As can be seen from the two graphs, if EMF () is asinusoidal graph then flux linkage must give a

cosine graph.

In fact the equations for each are...

N = BAN cos (or N = BAN cos t )

= BAN sin (or = BAN sin t )

(You do not need to know these equations howeverthey should make sense to you).


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Increasing the speed of rotation If the coil is rotated at a greater angular speed, the EMFgenerated will increase and the frequency of rotation willalso increase. Hence the graph will change in two ways.

Q5. The graph below shows the output of a coil rotating in afixed uniform magnetic field. On the same axes, sketch the

graph of i. a coil rotating with twice the frequency.ii. a coil rotating with half the frequency.


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Root Mean Square Current In mathematics the Root Mean Square (rms) is a

statistical method of determining the magnitude of aquantity that is varying. It can be thought of as akind of average value. In particular it is useful whendealing with sinusoidal variations (that can be

positive or negative) such as induced EMF andcurrent from a rotating coil.

For discrete values of any quantity the followingformula can be applied:


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Clearly the calculated value is the square root of themean of the squares of the discrete values.

Q6. Determine the rms value of current from thefollowing graph using eight successive discretevalues:

I (A)


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For electrical output from a coil rotating at constantspeed in a uniform magnetic field, the following

formulae can be applied: rms = 0

2

Irms = I02

Where...

0 = Maximum EMF (V) I0 = Maximum current (A)


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Power in AC circuits 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 tothe value of direct current that would dissipate powerat the same rate through a resistor.

Power = I rms x Vrms


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Q7. Determine a formula for average power in analternating circuit in terms of 0 and I 0.

Q8. The rms voltage in Europe is about 230V.Determine the peak voltage value.What will be the rms current value through a 20Wfluorescent light bulb?


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Transformers

If any two electrical circuits are near to each other, achanging current in one can cause an induced EMFin the other.

A transformer uses changing flux linkage produced

by one coil to induce an EMF in the second coil.

Primary

coil

Secondary

coil


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The input current is a.c.

Plot a graph of current in the primary (I p) againsttime. The flux in the core is proportional to I p.

Plot a graph of flux in the core against time.

The EMF induced in the secondary is proportionalto the rate of change of flux linkage.

Plot a graph of Induced EMF in the secondaryagainst time.


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Transformer Calculations

The flux passing through the primary and secondarycoils is identical in a 100% efficient transformer.Q. Explain (using Faradays Law) why having moreturns 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 thevoltages:

Vs NsVp Np

=


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Ideal Transformers

A 100% efficient transformer is known as an idealtransformer. In this case all the power on theprimary side is transferred to the secondary side.

Thus...

IpVp = IsVs (All values arerms values)


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Q. If Np < N s , which of the following are true (re-write the wrong statements):

a. p = s b. flux linkage is equal in both coils

c. I p > Is

d. V p > Vs


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Real Transformers

In reality the output power is less than the inputpower. This could be due to:- Resistance of wires (causing heat transfer)

- Eddy currents in core (causing heat transfer)

- Flux leakage (not linking into the secondary coil)

- Hysteresis (molecular friction) (causing heat

transfer)Q. Suggest a way of decreasing each of the firstthree losses.

(copper wires; laminated core; improved core design)


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47 alternating current

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