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V p = N p Δ Φ Δ t . size 12{V rSub { size 8{p} } = - N rSub { size 8{p} } { {ΔΦ} over {Δt} } } {}

The reason for this is a little more subtle. Lenz’s law tells us that the primary coil opposes the change in flux caused by the input voltage V p size 12{V rSub { size 8{p} } } {} , hence the minus sign (This is an example of self-inductance , a topic to be explored in some detail in later sections). Assuming negligible coil resistance, Kirchhoff’s loop rule tells us that the induced emf exactly equals the input voltage. Taking the ratio of these last two equations yields a useful relationship:

V s V p = N s N p . size 12{ { {V rSub { size 8{s} } } over {V rSub { size 8{p} } } } = { {N rSub { size 8{s} } } over {N rSub { size 8{p} } } } } {}

This is known as the transformer equation    , and it simply states that the ratio of the secondary to primary voltages in a transformer equals the ratio of the number of loops in their coils.

The output voltage of a transformer can be less than, greater than, or equal to the input voltage, depending on the ratio of the number of loops in their coils. Some transformers even provide a variable output by allowing connection to be made at different points on the secondary coil. A step-up transformer    is one that increases voltage, whereas a step-down transformer    decreases voltage. Assuming, as we have, that resistance is negligible, the electrical power output of a transformer equals its input. This is nearly true in practice—transformer efficiency often exceeds 99%. Equating the power input and output,

P p = I p V p = I s V s = P s . size 12{P rSub { size 8{p} } =I rSub { size 8{p} } V rSub { size 8{p} } =I rSub { size 8{s} } V rSub { size 8{s} } =P rSub { size 8{s} } } {}

Rearranging terms gives

V s V p = I p I s . size 12{ { {V rSub { size 8{s} } } over {V rSub { size 8{p} } } } = { {I rSub { size 8{p} } } over {I rSub { size 8{s} } } } } {}

Combining this with V s V p = N s N p size 12{ { {V rSub { size 8{s} } } over {V rSub { size 8{p} } } } = { {N rSub { size 8{s} } } over {N rSub { size 8{p} } } } } {} , we find that

I s I p = N p N s size 12{ { {I rSub { size 8{s} } } over {I rSub { size 8{p} } } } = { {N rSub { size 8{p} } } over {N rSub { size 8{s} } } } } {}

is the relationship between the output and input currents of a transformer. So if voltage increases, current decreases. Conversely, if voltage decreases, current increases.

Calculating characteristics of a step-up transformer

A portable x-ray unit has a step-up transformer, the 120 V input of which is transformed to the 100 kV output needed by the x-ray tube. The primary has 50 loops and draws a current of 10.00 A when in use. (a) What is the number of loops in the secondary? (b) Find the current output of the secondary.

Strategy and Solution for (a)

We solve V s V p = N s N p size 12{ { {V rSub { size 8{s} } } over {V rSub { size 8{p} } } } = { {N rSub { size 8{s} } } over {N rSub { size 8{p} } } } } {} for N s size 12{N rSub { size 8{s} } } {} , the number of loops in the secondary, and enter the known values. This gives

N s = N p V s V p = ( 50 ) 100,000 V 120 V = 4 . 17 × 10 4 . alignl { stack { size 12{N rSub { size 8{s} } =N rSub { size 8{p} } { {V rSub { size 8{s} } } over {V rSub { size 8{p} } } } } {} #" "= \( "50" \) { {"100,000 V"} over {"120"" V"} } =4 "." "17" times "10" rSup { size 8{4} } {} } } {}

Discussion for (a)

A large number of loops in the secondary (compared with the primary) is required to produce such a large voltage. This would be true for neon sign transformers and those supplying high voltage inside TVs and CRTs.

Strategy and Solution for (b)

We can similarly find the output current of the secondary by solving I s I p = N p N s size 12{ { {I rSub { size 8{s} } } over {I rSub { size 8{p} } } } = { {N rSub { size 8{p} } } over {N rSub { size 8{s} } } } } {} for I s size 12{I rSub { size 8{s} } } {} and entering known values. This gives

I s = I p N p N s = ( 10 . 00 A ) 50 4 . 17 × 10 4 = 12.0 mA . alignl { stack { size 12{I rSub { size 8{s} } =I rSub { size 8{p} } { {N rSub { size 8{p} } } over {N rSub { size 8{s} } } } } {} #" "= \( "10" "." "00 A" \) { {"50"} over {4 "." "17" times "10" rSup { size 8{4} } } } ="12" "." 0" mA" {} } } {}

Discussion for (b)

As expected, the current output is significantly less than the input. In certain spectacular demonstrations, very large voltages are used to produce long arcs, but they are relatively safe because the transformer output does not supply a large current. Note that the power input here is P p = I p V p = ( 10 . 00 A ) ( 120 V ) = 1 . 20 kW size 12{P rSub { size 8{p} } =I rSub { size 8{p} } V rSub { size 8{p} } = \( "10" "." "00"`A \) \( "120"`V \) =1 "." "20"`"kW"} {} . This equals the power output P p = I s V s = ( 12 . 0 mA ) ( 100 kV ) = 1 . 20 kW size 12{P rSub { size 8{p} } =I rSub { size 8{s} } V rSub { size 8{s} } = \( "12" "." 0`"mA" \) \( "100"`"kV" \) =1 "." "20"`"kW"} {} , as we assumed in the derivation of the equations used.

Got questions? Get instant answers now!

The fact that transformers are based on Faraday’s law of induction makes it clear why we cannot use transformers to change DC voltages. If there is no change in primary voltage, there is no voltage induced in the secondary. One possibility is to connect DC to the primary coil through a switch. As the switch is opened and closed, the secondary produces a voltage like that in [link] . This is not really a practical alternative, and AC is in common use wherever it is necessary to increase or decrease voltages.

Questions & Answers

how do you calculate the 5% uncertainty of 4cm?
melia Reply
4cm/100×5= 0.2cm
haider
how do you calculate the 5% absolute uncertainty of a 200g mass?
melia Reply
= 200g±(5%)10g
haider
use the 10g as the uncertainty?
melia
which topic u discussing about?
haider
topic of question?
haider
the relationship between the applied force and the deflection
melia
sorry wrong question i meant the 5% uncertainty of 4cm?
melia
its 0.2 cm or 2mm
haider
thank you
melia
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Chioma
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haider
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sean
hi
Noks
the meaning of phrase in physics
Chovwe Reply
is the meaning of phrase in physics
Chovwe
write an expression for a plane progressive wave moving from left to right along x axis and having amplitude 0.02m, frequency of 650Hz and speed if 680ms-¹
Gabriel Reply
how does a model differ from a theory
Friday Reply
To use the vocabulary of model theory and meta-logic, a theory is a set of sentences which can be derived from a formal model using some rule of inference (usually just modus ponens). So, for example, Number Theory is the set of sentences true about numbers. But the model is a structure together wit
Jesilda
with an iterpretation.
Jesilda
what is vector quantity
Ridwan Reply
Vector quality have both direction and magnitude, such as Force, displacement, acceleration and etc.
Besmellah
Is the force attractive or repulsive between the hot and neutral lines hung from power poles? Why?
Jack Reply
what's electromagnetic induction
Chinaza Reply
electromagnetic induction is a process in which conductor is put in a particular position and magnetic field keeps varying.
Lukman
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Salaudeen
what is mutual induction?
je
mutual induction can be define as the current flowing in one coil that induces a voltage in an adjacent coil.
Johnson
how to undergo polarization
Ajayi Reply
show that a particle moving under the influence of an attractive force mu/y³ towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v²k² and distance uk²/√u-vk as origin
Gabriel Reply
show that a particle moving under the influence of an attractive force mu/y^3 towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v^2k^2 and distance uk^2/√u-k as origin
Gabriel Reply
No idea.... Are you even sure this question exist?
Mavis
I can't even understand the question
Ademiye
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Gabriel
mu/y³ u>v²k² uk²/√u-vk please help me out
Gabriel
An engineer builds two simple pendula. Both are suspended from small wires secured to the ceiling of a room. Each pendulum hovers 2 cm above the floor. Pendulum 1 has a bob with a mass of 10kg . Pendulum 2 has a bob with a mass of 100 kg . Describe how the motion of the pendula will differ if the bobs are both displaced by 12º .
Imtiaz Reply
no ideas
Augstine
if u at an angle of 12 degrees their period will be same so as their velocity, that means they both move simultaneously since both both hovers at same length meaning they have the same length
Ademiye
Modern cars are made of materials that make them collapsible upon collision. Explain using physics concept (Force and impulse), how these car designs help with the safety of passengers.
Isaac Reply
calculate the force due to surface tension required to support a column liquid in a capillary tube 5mm. If the capillary tube is dipped into a beaker of water
Mildred Reply
find the time required for a train Half a Kilometre long to cross a bridge almost kilometre long racing at 100km/h
Ademiye
method of polarization
Ajayi
What is atomic number?
Makperr Reply
The number of protons in the nucleus of an atom
Deborah
Practice Key Terms 4

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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