Grade by Grade
F. Electricity and Magnetism · Electricity and Magnetism

Transformers: Stepping Voltage Up and Down

F3.8 F2.6 F3.7 F3.4About 75 minutes
Learning goals
  • I can describe the parts of a transformer and explain how it works using Faraday's law.
  • I can tell a step-up transformer from a step-down transformer.
  • I can solve problems relating potential difference, current, number of turns, power and energy in a transformer.
  • I can calculate a transformer's efficiency and explain where energy is lost.

Words to know

transformer
A device that changes the potential difference of an alternating current, using two coils wound on a common iron core.
primary coil
The input coil, connected to the AC supply (Nₚ turns, Vₚ, Iₚ).
secondary coil
The output coil, connected to the load (Nₛ turns, Vₛ, Iₛ).
step-up transformer
A transformer with more turns on the secondary than the primary (Nₛ > Nₚ), so Vₛ > Vₚ.
step-down transformer
A transformer with fewer turns on the secondary (Nₛ < Nₚ), so Vₛ < Vₚ.
ideal transformer
A transformer with no energy losses: power in equals power out (Pₚ = Pₛ).
eddy currents
Swirling induced currents in a solid metal core that waste energy as heat; reduced by building the core from thin insulated layers (laminations).

The box on the pole

Look up along a residential street and you will often see a grey cylinder on a hydro pole, or a green metal box on a lawn. These are transformers. Electricity may arrive in your neighbourhood at thousands of volts, but your outlets supply 120 V. The transformer does that change, quietly, with no moving parts. Your phone charger has a tiny transformer inside, too.

How a transformer works

A transformer has two coils of insulated wire wound on the same soft-iron core:

  • The primary coil is connected to the AC supply.
  • The secondary coil is connected to the load.

The alternating current in the primary makes a magnetic field in the core that is constantly changing: growing, shrinking and reversing 60 times a second. The iron core guides this changing field through the secondary coil. By Faraday's law, the changing field induces an alternating potential difference in the secondary.

No current flows directly from one coil to the other; energy passes through the changing magnetic field. With steady DC, the field would not change, and the secondary would get nothing (except a brief pulse when the current is switched on or off). That is why transformers need AC.

laminated soft-iron coreACinACoutprimary coil (Nₚ = 5)secondary coil (Nₛ = 10)changing fieldcirculates in core
A step-up transformer. The primary has fewer turns than the secondary. The AC in the primary makes a changing magnetic field that circulates around the iron core and induces AC in the secondary.

The transformer equations

Each turn of wire in the core gets the same induced voltage. So the voltage of each coil is proportional to its number of turns:

Vₛ ÷ Vₚ = Nₛ ÷ Nₚ

  • If Nₛ > Nₚ, the voltage goes up: a step-up transformer.
  • If Nₛ < Nₚ, it goes down: a step-down transformer.

Energy is conserved, so a transformer cannot give out more power than it takes in. For an ideal transformer (no losses):

Pₚ = Pₛ, so VₚIₚ = VₛIₛ, which gives Iₛ ÷ Iₚ = Nₚ ÷ Nₛ = Vₚ ÷ Vₛ

The current ratio is the inverse of the voltage ratio. Step the voltage up 10 times and the current goes down 10 times. Nothing is free.

The energy delivered in a time Δt is E = PΔt.

A quick check

In any transformer problem, the high-voltage side has the low current, and the coil with more turns has the higher voltage. If your answer breaks either rule, look for an inverted ratio.

Worked example

Example 1: Turns and voltage

A doorbell transformer has 1200 turns on its primary and 160 turns on its secondary. It is connected to 120 V AC. Find the secondary voltage. Is it step-up or step-down?

  1. Vₛ ÷ Vₚ = Nₛ ÷ Nₚ, so Vₛ = Vₚ × (Nₛ ÷ Nₚ).
  2. Vₛ = 120 V × (160 ÷ 1200) = 120 × 0.1333 = 16 V.
  3. Nₛ < Nₚ and the voltage goes down: step-down.

16 V; a step-down transformer.

Worked example

Example 2: Currents in an ideal transformer

An ideal transformer steps 120 V down to 12 V for a device that draws 2.0 A. Find (a) the turns ratio, (b) the power, (c) the primary current.

  1. (a) Nₚ ÷ Nₛ = Vₚ ÷ Vₛ = 120 ÷ 12 = 10 : 1 (10 primary turns for every secondary turn).
  2. (b) Pₛ = VₛIₛ = (12 V)(2.0 A) = 24 W. Ideal, so Pₚ = 24 W too.
  3. (c) Iₚ = Pₚ ÷ Vₚ = 24 ÷ 120 = 0.20 A. (Check: the current ratio 2.0 ÷ 0.20 = 10 is the inverse of the voltage ratio ✓.)

10 : 1; 24 W; 0.20 A.

Voltage120 Vprimary12 VsecondaryCurrent0.20 Aprimary2.0 AsecondaryPower24 Wprimary24 Wsecondary
Example 2 in bars. The voltage goes down 10 times, the current goes up 10 times, and the power stays the same in an ideal transformer.

Real transformers: efficiency

Real transformers are not perfect, though large ones come very close (often well above 95%). Energy is lost as thermal energy:

  • in the coils, because the copper wire has resistance (P = I²R);
  • in the core, from eddy currents (the changing field induces swirling currents in the iron itself). Building the core from thin, insulated sheets called laminations breaks up these currents;
  • in the core again, from repeatedly re-aligning the magnetic domains (called hysteresis).

Efficiency = Pₛ ÷ Pₚ × 100% (useful power out ÷ power in)

Large transformers are cooled with oil or fans to carry away this heat.

Worked example

Example 3: Efficiency and energy lost

A transformer takes in 500 W and delivers 470 W. (a) Find its efficiency. (b) How much energy is lost as heat in 2.0 h?

  1. (a) Efficiency = 470 ÷ 500 × 100% = 94%.
  2. (b) Power lost = 500 − 470 = 30 W. Δt = 2.0 h × 3600 s/h = 7200 s.
  3. E_lost = PΔt = (30 W)(7200 s) = 2.2 × 10⁵ J (or 0.060 kW·h).

94%; about 2.2 × 10⁵ J lost.

Worked example

Example 4: A real step-up transformer

A 96% efficient transformer has 200 primary turns and 5000 secondary turns. The primary is connected to 240 V AC and draws 5.0 A. Find the secondary voltage and current.

  1. Vₛ = 240 × (5000 ÷ 200) = 240 × 25 = 6000 V (6.0 kV).
  2. Pₚ = VₚIₚ = (240)(5.0) = 1200 W. Pₛ = 0.96 × 1200 = 1152 W.
  3. Iₛ = Pₛ ÷ Vₛ = 1152 ÷ 6000 ≈ 0.19 A.

6.0 kV and about 0.19 A.

Just for fun

Not that kind of transformer: these never turn into trucks. They do hum, though. The low hum near a big transformer comes from its iron core changing shape very slightly as it magnetizes one way and then the other, 120 times a second.

Hands-on activity

Transformer detective

You need: two or three plug-in adapters ("wall warts") or laptop or phone chargers, paper and a calculator. Optional: the free PhET simulation "Faraday's Electromagnetic Lab", which has a transformer tab. Grown-up note: read the labels with everything unplugged. Never open a charger: the inside can hold a dangerous charge even when unplugged.

  1. Find each adapter's input (for example "120 V ~ 60 Hz 0.3 A"; the symbol ~ means AC) and output (for example "9 V ⎓ 1 A"; ⎓ means DC).
  2. Calculate the ratio of input voltage to output voltage. Older, heavy adapters contain a transformer with roughly this turns ratio, plus parts that change AC to DC.
  3. Calculate the maximum output power, P = VI.
  4. In the simulation, change the number of turns on the secondary coil and watch the bulb.

What to look for: ratios such as 120 V ÷ 9 V ≈ 13, which would need about 13 primary turns for every secondary turn. The input current printed on a label is a maximum rating, so you cannot get an accurate efficiency from labels alone. Modern light chargers use fast electronic switching with a very small transformer, which is why they are so light. In the simulation, more secondary turns make the bulb brighter, and the bulb lights only with AC (or while the magnet or current is changing).

Your turn

1

A transformer has 200 primary turns and 1000 secondary turns. The primary voltage is 12 V AC. Find the secondary voltage. Step-up or step-down?

2

A transformer steps 120 V down to 6.0 V. Its primary has 800 turns. How many turns are on the secondary?

3

An ideal transformer has Vₚ = 240 V and Iₚ = 0.50 A. Its secondary voltage is 12 V. Find the power and the secondary current.

4

Why does a transformer not work with a steady DC supply?

5

Why is a transformer core made of thin insulated layers instead of a solid block of iron?

6

A transformer takes in 200 W and delivers 190 W. Find its efficiency.

7

A generator's 20 kV output goes into a step-up transformer with a turns ratio Nₛ : Nₚ = 25 : 1. Find the output voltage.

More practice: warm-up

1

Nₛ = 50 and Nₚ = 500. Step-up or step-down?

2

What material is a transformer core made of, and why?

3

In an ideal transformer, how do the input power and output power compare?

4

If a transformer steps the voltage up by a factor of 5, what happens to the current (ideal case)?

5

Give one cause of energy loss in a real transformer.

More practice: on your own

1

A charger's transformer steps 120 V down to 6.0 V. Its primary has 1000 turns. The output current is 1.5 A. Assuming it is ideal, find the secondary turns and the primary current.

2

A 92% efficient transformer takes in 600 W. Its secondary voltage is 24 V. Find the output power and the secondary current.

3

A transformer's primary has 120 V and 2.0 A. Its secondary has 2400 V and 0.095 A. Find its efficiency.

4

A friend says a step-up transformer "creates energy because the voltage goes up." Explain why this is wrong.

5

A transformer takes in 1.5 kW and is 97% efficient. How much energy does it waste in one day, in kW·h and in joules?

Challenge

1

A transformer with 400 primary turns and 100 secondary turns has its primary connected (a) to a 12 V battery, then (b) to a 12 V AC supply. What does a voltmeter on the secondary read in each case?

2

A 12 V, 60 W lamp is run from a 120 V supply through an ideal transformer. Find the turns ratio, the lamp current, the primary current and the lamp's resistance.

3

A 95% efficient transformer steps 120 V down to 9.0 V and supplies 1.8 A. Find the primary current.

Check your understanding

Quiz

1.

Why does a transformer need alternating current?

2.

A transformer has Nₚ = 100 and Nₛ = 2000. The primary voltage is 120 V. What is the secondary voltage?

3.

In an ideal step-up transformer, the secondary current is…

4.

An ideal transformer delivers 12 V and 3.0 A from a 120 V supply. What is the primary current?

5.

Why is a transformer core laminated?

6.

A transformer has input power 800 W and output power 760 W. What is its efficiency?

For parents and teachers

Big idea: Transformers use electromagnetic induction to step AC voltage up or down (F3.8). Students solve problems linking potential difference, current, number of turns, power and energy (F2.6). Conservation of energy is the key idea: when voltage goes up, current goes down.

How to help: Reading the labels on chargers is a quick, safe link to real life; keep them unplugged and never open them. Ask your teen to say each answer as a sentence: "The voltage went down 10 times, so the current went up 10 times."

Common difficulties:

  • Inverting the turns ratio. Remember: more turns, more voltage.
  • Applying the voltage ratio to current. Current goes the opposite way.
  • Thinking transformers work with batteries. They need AC.
  • Forgetting that efficiency uses power (or energy), not voltage alone.