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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

A proton initially at rest falls through a p.d of 25000V. what speed does it gain?
Minister Reply
what is the reaction of heat on magnet
ORIZINO Reply
what is a physical significant of electric dipole moment .
PRANAB Reply
A dipole moment it's a mechanical electrical effect used in nature
Antonio
what is the uses of carbon brushes in generator
Malik Reply
at what temperature is the degree Fahrenheit equal to degree Celsius
Grace Reply
Celsius and Faharaneith are different, never equal
Antonio
find their liners express of n=a+b/T² ( plot graph n against T)
Donsmart Reply
Radio Stations often advertis "instant news,,if that meens you can hear the news the instant the radio announcer speaks it is the claim true? what approximate time interval is required for a message to travel from Cairo to Aswan by radio waves (500km) (Assume the waves Casbe detected at this range )
mahmod Reply
what is growth and decay
Pawan Reply
thevenin
Oladejo Reply
Can someone please predict the trajectory of a point charge in a uniform electric field????
erlinda Reply
what is deference between strong force and coulomb force
zahid Reply
so basically the electric lines or the field lines
zach Reply
it's the measure of the flow of an electric field through a certain area
zach Reply
What is electric flux
Pranju Reply
how to calculate the magnetic force if the B field is depend on the coordinate
Ivan 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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