please follow the instruction on the pdf then you are good to start. Objective: Review Maxwell’s equations and applications: AC generator, motor,
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AC CURRENT LAB
Objective: Review Maxwell’s equations and applications: AC generator, motor,
Theory: Refer to chapters 30 & 31 of Resnik and Halliday
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
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
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
𝐼2 = 𝐼1
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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