ElectromagnetismElectromagnetism

Topic Topic 12.2 Alternating Current12.2 Alternating Current

Rotating CoilsRotating Coils

Most of our electricity comes from huge Most of our electricity comes from huge generators in power stations.generators in power stations.

There are smaller generators in cars and There are smaller generators in cars and on some bicycles.on some bicycles.

These generators, or dynamos, all use These generators, or dynamos, all use electromagnetic induction.electromagnetic induction.

When turned, they induce an EMF When turned, they induce an EMF (voltage) which can make a current flow.(voltage) which can make a current flow.

The next diagram shows a simple AC generator.The next diagram shows a simple AC generator. It is providing the current for a small bulb.It is providing the current for a small bulb. The coil is made of insulated copper wire and is The coil is made of insulated copper wire and is

rotated by turning the shaft.rotated by turning the shaft. The The slip rings slip rings are fixed to the coil and rotate are fixed to the coil and rotate

with it.with it. The The brushes brushes are two contacts which rub against are two contacts which rub against

the slip rings and keep the coil connected to the the slip rings and keep the coil connected to the outside part of the circuit.outside part of the circuit.

They are usually made of carbon.They are usually made of carbon.

AC GeneratorAC Generator

When the coil is rotated, it cuts magnetic field When the coil is rotated, it cuts magnetic field lines, so an EMF is generated.lines, so an EMF is generated.

This makes a current flow.This makes a current flow. As the coil rotates, each side travels upwards, As the coil rotates, each side travels upwards,

downwards, upwards, downwards... and so on, downwards, upwards, downwards... and so on, through the magnetic field.through the magnetic field.

So the current flows backwards, forwards... and So the current flows backwards, forwards... and so on.so on.

In other words, it is AC.In other words, it is AC.

The graph shows how the current varies The graph shows how the current varies through one cycle (rotation).through one cycle (rotation).

It is a maximum when the coil is horizontal It is a maximum when the coil is horizontal and cutting field lines at the fastest rate.and cutting field lines at the fastest rate.

It is zero when the coil is vertical and It is zero when the coil is vertical and cutting no field lines.cutting no field lines.

AC Generator OutputAC Generator Output

The Sinusoidal ShapeThe Sinusoidal Shape

As the emf can be calculated fromAs the emf can be calculated from εε = - N = - N Δ Δ ((ΦΦ/ / ΔΔt)t) and and ΦΦ = AB cos = AB cos θθ It can be clearly seen that the shape of the curve It can be clearly seen that the shape of the curve

must be sinusoidal.must be sinusoidal.

The following all increase the maximum The following all increase the maximum EMF (and the current): EMF (and the current):

increasing the number of turns on the coilincreasing the number of turns on the coil increasing the area of the coilincreasing the area of the coilusing a stronger magnetusing a stronger magnet rotating the coil faster.rotating the coil faster. ((rotating the coil faster increases the rotating the coil faster increases the

frequency too!)frequency too!)

Alternating CurrentAlternating Current

The graph shows the values of V and I The graph shows the values of V and I plotted against timeplotted against time

Can you see that the graphs for both V Can you see that the graphs for both V and I are sine curves?and I are sine curves?

They both vary sinusoidally with time.They both vary sinusoidally with time. Can you see that the p.d. and the current Can you see that the p.d. and the current

rise and fall rise and fall together?together? We say that V and I are in phase.We say that V and I are in phase.

The time period T of an alternating p.d. or The time period T of an alternating p.d. or current is the time for one complete cycle. This current is the time for one complete cycle. This is shown on the graphis shown on the graph

The frequency f of an alternating pd or current is The frequency f of an alternating pd or current is the number of cycles in one second.the number of cycles in one second.

The peak values VThe peak values V00 and I and I00 of the alternating p.d. of the alternating p.d. and current are also shown on the graphand current are also shown on the graph

Root Mean Square ValuesRoot Mean Square Values

How do we measure the size of an How do we measure the size of an alternating p.d. (or current) when its value alternating p.d. (or current) when its value changes from one instant to the next?changes from one instant to the next?

We could use the peak value, but this We could use the peak value, but this occurs only for a moment.occurs only for a moment.

What about the average value?What about the average value?This is zero over a complete cycle and so This is zero over a complete cycle and so

is not very helpful!is not very helpful!

In fact, we use the In fact, we use the root‑mean‑square root‑mean‑square (r.m.s.) (r.m.s.) value.value.

This is also called the This is also called the effective value.effective value.The r.m.s. value is chosen, because it is The r.m.s. value is chosen, because it is

the value which is the value which is equivalent to a steady equivalent to a steady direct current.direct current.

You can investigate this using the You can investigate this using the apparatus in the diagramapparatus in the diagram

Place two identical lamps side by side.Place two identical lamps side by side.Connect one lamp to a battery; the other Connect one lamp to a battery; the other

to an a.c. supply.to an a.c. supply.The p.d. across each lamp must be The p.d. across each lamp must be

displayed on the screen of a double‑beam displayed on the screen of a double‑beam oscilloscope.oscilloscope.

Adjust the a.c. supply, so that both lamps Adjust the a.c. supply, so that both lamps are equally brightare equally bright

The graph shows a typical trace from the The graph shows a typical trace from the oscilloscope We can use it to compare the oscilloscope We can use it to compare the voltage across each lamp.voltage across each lamp.

Since both lamps are equally bright, the d.c. and Since both lamps are equally bright, the d.c. and a.c. supplies are transferring energy to the bulbs a.c. supplies are transferring energy to the bulbs at the same rate.at the same rate.

Therefore, the d.c. voltage is equivalent to the Therefore, the d.c. voltage is equivalent to the a.c. voltage.a.c. voltage.

The d.c. voltage equals the r.m.s. value of the The d.c. voltage equals the r.m.s. value of the a.c. voltage.a.c. voltage.

Notice that the r.m.s. value is about 70% (1/Notice that the r.m.s. value is about 70% (1/√2)√2) of the peak value.of the peak value.

In fact:In fact:

Why Why √2√2

Why The power dissipated in a lamp Why The power dissipated in a lamp varies as the p.d. across it, and the current varies as the p.d. across it, and the current passing through it, alternate.passing through it, alternate.

Remember power,P = current,(Remember power,P = current,(I)I) x p.d., x p.d., (V)(V)

If we multiply the values of I and V at any If we multiply the values of I and V at any instant, we get the power at that moment instant, we get the power at that moment in time, as the graph showsin time, as the graph shows

The power varies between IThe power varies between I00VV00 and zero. and zero.

Therefore Therefore average power = Iaverage power = I00VV00 / 2 / 2

Or P = (Or P = (II0 0 / / √√ 2) x (V 2) x (V00 / / √√ 2) 2)

Or P = IOr P = Irms x rms x VVrmsrms

Root Mean Square VoltageRoot Mean Square Voltage

Root Mean Square CurrentRoot Mean Square Current

CalculationsCalculations

Use the rms values in the normal Use the rms values in the normal equations}equations}

VVrmsrms = I = Irmsrms R R

P = IP = Irmsrms V Vrmsrms

P = IP = Irmsrms2 2 RR

P = VP = Vrmsrms2 2 / R/ R

TransformersTransformers

A transformer changes the value of an A transformer changes the value of an alternating voltage.alternating voltage.

It consists of two coils, wound around a It consists of two coils, wound around a soft‑iron core, as shownsoft‑iron core, as shown

In this transformer, when an input p.d. of 2 In this transformer, when an input p.d. of 2 V is applied to the primary coil, the output V is applied to the primary coil, the output ppdd. of the secondary coil is 8V. of the secondary coil is 8V

How does the transformer How does the transformer work? work?

An alternating current flows in the primary coil. An alternating current flows in the primary coil. This produces an alternating magnetic field in This produces an alternating magnetic field in

the soft iron core.the soft iron core. This means that the flux linkage of the This means that the flux linkage of the

secondary coil is constantly changing and so an secondary coil is constantly changing and so an alternating potential difference is induced across alternating potential difference is induced across it.it.

A transformer cannot work on d.c. A transformer cannot work on d.c.

An Ideal TransformerAn Ideal Transformer

This is 100% efficientThis is 100% efficientTherefore the power in the primary is Therefore the power in the primary is

equal to the power in the secondaryequal to the power in the secondaryPPpp = P = Pss

i.e. Ii.e. Ip p VVpp = I = Is s VVss

Step-up Step-downStep-up Step-down

A step‑up transformer increases the a.c. A step‑up transformer increases the a.c. voltage, because the secondary coil has voltage, because the secondary coil has more turns than the primary coil.more turns than the primary coil.

In a step‑down transformer, the voltage is In a step‑down transformer, the voltage is reduced and the secondary coil has fewer reduced and the secondary coil has fewer turns than the primary coil.turns than the primary coil.

The EquationThe Equation

Note:Note: • • In the transformer equations, the In the transformer equations, the

voltages and currents that you use must voltages and currents that you use must all be peak values or all r.m.s. values. all be peak values or all r.m.s. values.

Do not mix the two.Do not mix the two.Strictly, the equations apply only to an Strictly, the equations apply only to an

ideal transformer, which is 100 % efficient.ideal transformer, which is 100 % efficient.