15.6 Transformers (Page 3/9)

University physics volume 2 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	$v = V_{0} sin ω t$
AC current	$i = I_{0} sin ω t$
capacitive reactance	$\frac{V_{0}}{I_{0}} = \frac{1}{ω C} = X_{C}$
rms voltage	$V_{rms} = \frac{V_{0}}{\sqrt{2}}$
rms current	$I_{rms} = \frac{I_{0}}{\sqrt{2}}$
inductive reactance	$\frac{V_{0}}{I_{0}} = ω L = X_{L}$
Phase angle of an ac circuit	$ϕ = {tan}^{−1} \frac{X_{L} - X_{C}}{R}$
AC version of Ohm’s law	$I_{0} = \frac{V_{0}}{Z}$
Impedance of an ac circuit	$Z = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}$
Average power associated with a circuit element	$P_{ave} = \frac{1}{2} I_{0} V_{0} cos ϕ$
Average power dissipated by a resistor	$P_{ave} = \frac{1}{2} I_{0} V_{0} = I_{rms} V_{rms} = I_{rms}^{2} R$
Resonant angular frequency of a circuit	$ω_{0} = \sqrt{\frac{1}{L C}}$
Quality factor of a circuit	$Q = \frac{ω_{0}}{Δ ω}$
Quality factor of a circuit in terms of the circuit parameters	$Q = \frac{ω_{0} L}{R}$
Transformer equation with voltage	$\frac{V_{S}}{V_{P}} = \frac{N_{S}}{N_{P}}$
Transformer equation with current	$I_{S} = \frac{N_{P}}{N_{S}} I_{P}$

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

differentiate between demand and supply giving examples

Lambiv Reply

differentiated between demand and supply using examples

Lambiv

what is labour ?

Lambiv

how will I do?

Venny Reply

how is the graph works?I don't fully understand

Rezat Reply

information

Eliyee

devaluation

Eliyee

WARKISA

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Lambiv

multiple choice question

Aster Reply

appreciation

Eliyee

explain perfect market

Lindiwe Reply

In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,

Ezea

What is ceteris paribus?

Shukri Reply

other things being equal

AI-Robot

When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab

Kelo

Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)

Kelo

yes,thank you

Shukri

Can I ask you other question?

Shukri

what is monopoly mean?

Habtamu Reply

What is different between quantity demand and demand?

Shukri Reply

Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded

Ezea

Shukri

how do you save a country economic situation when it's falling apart

Lilia Reply

what is the difference between economic growth and development

Fiker Reply

Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.

Shukri

production function means

Jabir

What do you think is more important to focus on when considering inequality ?

Abdisa Reply

any question about economics?

Awais Reply

sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏

Asui

it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs

Awais

thank you so much 👍 sir

Asui

In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p

Cornelius

Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .

Feyisa Reply

Answer

Feyisa

Jabir

the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema

Gsbwnw Reply

suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product

Abdureman

types of unemployment

Yomi Reply

What is the difference between perfect competition and monopolistic competition?

Mohammed

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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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