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please follow the instruction on the pdf then you are good to start. Objective: Review Maxwell’s equations and applications: AC generator, motor,

and transformer.

Student’s name: _________________________ Grade: _______

AC CURRENT LAB

Objective: Review Maxwell’s equations and applications: AC generator, motor,

and transformer.

Theory: Refer to chapters 30 & 31 of Resnik and Halliday

Introduction:

Maxwell’s equations are thought of as the mathematical summary of the classical

theory of electromagnetism. They describe how both electric and magnetic fields

arise from electric charge and currents, how they propagate and how they influence

each other.

These equations, along with the Lorentz force, quantify 99.99% of the physical

processes that you experience, including touch, taste, sight and the neurological

process of thinking itself.

They are a concise set of equations that completely specify the electric and

magnetic fields, thanks to the Fundamental Theorem of Vector Calculus.

This theorem says that if you know both the curl and divergence of a vector field

everywhere, then there is a formula to calculate the field itself from these values.

Maxwell’s equations give us the divergence and curl of the electric and magnetic

fields (4 equations) in terms of the charges and currents.

Thus, if you can figure out what all the overall distribution of electric charges

are and how they are moving, then you can immediately calculate both the

electric and magnetic fields for any situation.

It was through the synthesis of Maxwell’s equations that we realized that light is an

electromagnetic wave. In the 19th century, physicists realized that there were

solutions to Maxwell’s equations in which electric and magnetic fields could

exist together in the absence of electric charge.

This solution was an oscillating, traveling wave, moving at 3×108 meters per

second. Experiments revealed that light itself moved at exactly the same speed.

This was not a coincidence – they were the same thing. We could make light

through the manipulation of electric charges. This resulted in the creation of manmade light sources, such as radios (radio waves are a low energy form of light),

lasers and synchrotrons.

Our lives in the modern era depend critically on our understanding of Maxwell’s

equations. Without it, things like cell phones, computers and electrical power

would not be impossible. (Daniel Merthe, USC)

Waves transfer energy. Average energy transfer over one cycle of oscillation is

called wave’s intensity I.

I = P/A

P is the power (energy transferred per second) of a wave that impinges on area A.

If a source with power P emits electromagnetic waves uniformly in all directions,

the electromagnetic wave intensity at distance r from the source is:

I = P/(4πr2) = (𝑐𝜀𝑜 /2)𝐸𝑜2

Electric field amplitude and magnetic field amplitude are related:

Eo = cBo

Generator: Generator is a device that transforms mechanical energy to electrical

energy, typically by electromagnetic induction via Faraday’s Law.

Motor: An electric motor converts electrical energy into mechanical energy

(Lorent’s force)

AC Transformer:

An AC transformer is an electrical device that is used to change the voltage in

AC electrical circuits. A transformer (assumed to be ideal) is an iron core on

which are wound a primary coil of N 1 turns and a secondary coil of N2 turns. If

the primary coil is connected across an AC generator, the primary and secondary

voltages/currents are related by:

𝑉2 = 𝑉1

𝑁2

𝑁1

𝐼2 = 𝐼1

𝑁1

𝑁2

One of the great advantages of AC over DC for electric power distribution is that

it is much easier to step voltage levels up and down with AC than with DC. For

long distance power transmission it is desirable to use as high a voltage and as

small a current as possible. This reduces power (P=RI 2) loses (Ohmic losses) in

the transmission lines, and smaller wires can be used, saving on material costs.

QUESTIONS (15 points)

Question 1: (3 points) Open the AC generator simulation

Click “StepByStep Animation” button. Explain in detail how the generator works

and explain the shape of the graph of voltage vs. time (for 4 steps).

Question 2: (3 points) What are advantages of AC current, explain? (List more

than four advantages)

Question 3: (3 points)

A digital cell phone broadcasts a 0.6 W signal at a frequency of 1.9 GHz. What are

the amplitudes of the electric and magnetic fields at a distance of 10 cm, about the

distance to the center of the user’s brain?

Question 4: (6 points) Electricity is distributed from electrical substations to

neighborhoods at 15,000 V. This is a 60 Hz oscillating AC voltage.

Neighborhood transformers, seen on utility poles, step this voltage down to the

120 V that is delivered to your house.

A. How many turns does the primary coil on the transformer have if the

secondary coil has 100 turns?

B. No energy is lost in an ideal transformer, so the output power from the

secondary coil equals the input power to the primary coil. Suppose a

neighborhood transformer delivers 250 A at 120 V. What is the current in

the 15,000 V line from substation?

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