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Summary

  • Power plants transmit high voltages at low currents to achieve lower ohmic losses in their many kilometers of transmission lines.
  • Transformers use induction to transform voltages from one value to another.
  • For a transformer, the voltages across the primary and secondary coils, or windings, are related by the transformer equation.
  • The currents in the primary and secondary windings are related by the number of primary and secondary loops, or turns, in the windings of the transformer.
  • A step-up transformer increases voltage and decreases current, whereas a step-down transformer decreases voltage and increases current.

Key equations

AC voltage v = V 0 sin ω t
AC current i = I 0 sin ω t
capacitive reactance V 0 I 0 = 1 ω C = X C
rms voltage V rms = V 0 2
rms current I rms = I 0 2
inductive reactance V 0 I 0 = ω L = X L
Phase angle of an ac circuit ϕ = tan −1 X L X C R
AC version of Ohm’s law I 0 = V 0 Z
Impedance of an ac circuit Z = R 2 + ( X L X C ) 2
Average power associated with a circuit element P ave = 1 2 I 0 V 0 cos ϕ
Average power dissipated by a resistor P ave = 1 2 I 0 V 0 = I rms V rms = I rms 2 R
Resonant angular frequency of a circuit ω 0 = 1 L C
Quality factor of a circuit Q = ω 0 Δ ω
Quality factor of a circuit in terms of the circuit parameters Q = ω 0 L R
Transformer equation with voltage V S V P = N S N P
Transformer equation with current I S = N P N S I P

Conceptual questions

Why do transmission lines operate at very high voltages while household circuits operate at fairly small voltages?

There is less thermal loss if the transmission lines operate at low currents and high voltages.

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How can you distinguish the primary winding from the secondary winding in a step-up transformer?

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Battery packs in some electronic devices are charged using an adapter connected to a wall socket. Speculate as to the purpose of the adapter.

The adapter has a step-down transformer to have a lower voltage and possibly higher current at which the device can operate.

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Will a transformer work if the input is a dc voltage?

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Why are the primary and secondary coils of a transformer wrapped around the same closed loop of iron?

so each loop can experience the same changing magnetic flux

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Problems

A step-up transformer is designed so that the output of its secondary winding is 2000 V (rms) when the primary winding is connected to a 110-V (rms) line voltage. (a) If there are 100 turns in the primary winding, how many turns are there in the secondary winding? (b) If a resistor connected across the secondary winding draws an rms current of 0.75 A, what is the current in the primary winding?

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A step-up transformer connected to a 110-V line is used to supply a hydrogen-gas discharge tube with 5.0 kV (rms). The tube dissipates 75 W of power. (a) What is the ratio of the number of turns in the secondary winding to the number of turns in the primary winding? (b) What are the rms currents in the primary and secondary windings? (c) What is the effective resistance seen by the 110-V source?

a. 45:1; b. 0.68 A, 0.015 A; c. 160 Ω

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An ac source of emf delivers 5.0 mW of power at an rms current of 2.0 mA when it is connected to the primary coil of a transformer. The rms voltage across the secondary coil is 20 V. (a) What are the voltage across the primary coil and the current through the secondary coil? (b) What is the ratio of secondary to primary turns for the transformer?

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Questions & Answers

determining dimensional correctness
PATRICK Reply
determine dimensional correctness of,T=2π√L/g
PATRICK
somebody help me answer the question above
PATRICK
calculate the heat flow per square meter through a mineral roll insulation 5cm thick if the temperature on the two surfaces are 30degree Celsius and 20 degree Celsius respectively. thermal conduction of mineral roll is 0.04
akuribire Reply
what are the elementary compositions of a cell?
jackson Reply
when a current pass through a material does the velocity varies
lovet Reply
what is spin entropy ?and disorder in ferromagnetic material
Nepal Reply
diagram of an hall effect sensor
Aweda Reply
if a magnetised wire having dipole moment M is bent in the form of arc subtending angle of 45°at centre,new magnetic moment is
Pravin Reply
is this book for preparing IIT or neet?
jyotirmayee Reply
is it possible to increase the temperature of a gas without adding heat to it?
gurpreet Reply
I'm not sure about it, but I think it's possible. If you add some form of energy to the system, it's a possibility. Also, if you change the pression or the volume of the system, you'll increase the kinetic energy of the system, increasing the gas temperature. I don't know if I'm correct.
playdoh
For example, if you get a syringe and close the tip(sealing the air inside), and start pumping the plunger, you'll notice that it starts getting hot. Again, I'm not sure if I am correct.
playdoh
you are right for example an adiabatic process changes all variables without external energy to yield a temperature change. (Search Otto cycle)
Brad
when a current pass through a material does the velocity varies
lovet
yes at adiabatic compression temperature increase
Nepal
how to draw a diagram of a triode
Ssempala Reply
whate is fckg diagrame?
Arzoodan
why do we use integration?
Monalisa Reply
To know surfaces below graphs.
Jan
To find a Primitive function. Primitive function: a function that is the origin of another
playdoh
yes
Dharmdev
what is laps rate
Dharmdev
Г=-dT/dZ that is simply defination
Arzoodan
what is z
Dharmdev
to find the area under a graph or to accumulate .e.g. sum of momentum over time is no etic energy.
Naod
Z is alt.,dZ altv difference
Arzoodan
what is the Elasticty
Heeran Reply
it is the property of the by virtue of it regains it's original shape after the removal of applied force (deforming force).
Prema
property of the material
Prema
which type of cable is suitable for patrol station wiring
Eric Reply
what is calorimeter
odionyenma Reply
heat measuring device
Suvransu
What is mean electric potential
Biren Reply
Practice Key Terms 4

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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