# 15.6 Transformers  (Page 3/9)

 Page 3 / 9

## 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 $v={V}_{0}\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\omega t$ AC current $i={I}_{0}\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\omega t$ capacitive reactance $\frac{{V}_{0}}{{I}_{0}}=\frac{1}{\omega C}={X}_{C}$ rms voltage ${V}_{\text{rms}}=\frac{{V}_{0}}{\sqrt{2}}$ rms current ${I}_{\text{rms}}=\frac{{I}_{0}}{\sqrt{2}}$ inductive reactance $\frac{{V}_{0}}{{I}_{0}}=\omega L={X}_{L}$ Phase angle of an ac circuit $\varphi ={\text{tan}}^{-1}\frac{{X}_{L}-{X}_{C}}{R}$ AC version of Ohm’s law ${I}_{0}=\frac{{V}_{0}}{Z}$ Impedance of an ac circuit $Z=\sqrt{{R}^{2}+{\left({X}_{L}-{X}_{C}\right)}^{2}}$ Average power associated with a circuit element ${P}_{\text{ave}}=\frac{1}{2}{I}_{0}{V}_{0}\phantom{\rule{0.2em}{0ex}}\text{cos}\phantom{\rule{0.2em}{0ex}}\varphi$ Average power dissipated by a resistor ${P}_{\text{ave}}=\frac{1}{2}{I}_{0}{V}_{0}={I}_{\text{rms}}{V}_{\text{rms}}={I}_{\text{rms}}^{2}R$ Resonant angular frequency of a circuit ${\omega }_{0}=\sqrt{\frac{1}{LC}}$ Quality factor of a circuit $Q=\frac{{\omega }_{0}}{\text{Δ}\omega }$ Quality factor of a circuit in terms of the circuit parameters $Q=\frac{{\omega }_{0}L}{R}$ Transformer equation with voltage $\frac{{V}_{\text{S}}}{{V}_{\text{P}}}=\frac{{N}_{\text{S}}}{{N}_{\text{P}}}$ Transformer equation with current ${I}_{\text{S}}=\frac{{N}_{\text{P}}}{{N}_{\text{S}}}{I}_{\text{P}}$

## 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.

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

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.

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

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

## 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?

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. $160\phantom{\rule{0.2em}{0ex}}\text{Ω}$

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?

what is thermodynamics
the study of heat an other form of energy.
John
heat is internal kinetic energy of a body but it doesnt mean heat is energy contained in a body because heat means transfer of energy due to difference in temperature...and in thermo-dynamics we study cause, effect, application, laws, hypothesis and so on about above mentioned phenomenon in detail.
ing
It is abranch of physical chemistry which deals with the interconversion of all form of energy
Vishal
what is colamb,s law.?
it is a low studied the force between 2 charges F=q.q\r.r
Mostafa
what is the formula of del in cylindrical, polar media
prove that the formula for the unknown resistor is Rx=R2 x R3 divided by R3,when Ig=0.
what is flux
Total number of field lines crossing the surface area
Kamru
Basically flux in general is amount of anything...In Electricity and Magnetism it is the total no..of electric field lines or Magnetic field lines passing normally through the suface
prince
what is temperature change
Celine
a bottle of soft drink was removed from refrigerator and after some time, it was observed that its temperature has increased by 15 degree Celsius, what is the temperature change in degree Fahrenheit and degree Celsius
Celine
process whereby the degree of hotness of a body (or medium) changes
Salim
Q=mcΔT
Salim
where The letter "Q" is the heat transferred in an exchange in calories, "m" is the mass of the substance being heated in grams, "c" is its specific heat capacity and the static value, and "ΔT" is its change in temperature in degrees Celsius to reflect the change in temperature.
Salim
what was the temperature of the soft drink when it was removed ?
Salim
15 degree Celsius
Celine
15 degree
Celine
ok I think is just conversion
Salim
15 degree Celsius to Fahrenheit
Salim
0 degree Celsius = 32 Fahrenheit
Salim
15 degree Celsius = (15×1.8)+32 =59 Fahrenheit
Salim
I dont understand
Celine
the question said you should convert 15 degree Celsius to Fahrenheit
Salim
To convert temperatures in degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.
Salim
what is d final ans for Fahrenheit and Celsius
Celine
it said what is temperature change in Fahrenheit and Celsius
Celine
the 15 is already in Celsius
Salim
So the final answer for Fahrenheit is 59
Salim
what is d final ans for Fahrenheit and Celsius
Celine
what are the effects of placing a dielectric between the plates of a capacitor
increase the capacitance.
Jorge
besides increasing the capacitance, is there any?
Bundi
mechanical stiffness and small size
Jorge
why for an ideal gas internal energy is directly proportional to thermodynamics temperature?
two charged particles are 8.45cm apart. They are moved and the force on each of them is found to have tripled. How far are they now?
what is flux
Bundi
Bundi, flux is the number of electric field crossing a surface area
Mubanga
you right
martin,F/F=(r×r)÷(r×r)
Mostafa
determining dimensional correctness
determine dimensional correctness of,T=2π√L/g
PATRICK
somebody help me answer the question above
PATRICK
d=dQ+w
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
what are the elementary compositions of a cell?
poles, chemical
prabir
when a current pass through a material does the velocity varies
no.
prabir
what is spin entropy ?and disorder in ferromagnetic material
diagram of an hall effect sensor
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
prabir