Motors and Generators

The video lesson for this topic is coming soon.

Essential Question

How do we turn electricity into motion, and motion into electricity?

Every fan, blender, and electric car uses a motor, and almost all of our electricity comes from generators. By the end of this lesson, you should be able to explain how motors, generators, and transformers work, and solve transformer problems with V_s/V_p = N_s/N_p.

Electric Motors

A current loop sits in a magnetic field
The field pushes its sides opposite ways
So the loop spins

End-on view of a wire loop between a north pole on the left and a south pole on the right, with blue field lines pointing right. The loop's left wire carries current out of the page and is pushed up. The right wire carries current into the page and is pushed down. A curved arrow shows the loop turning clockwise.

An electric motor is a loop (or coil) of wire carrying current in a magnetic field. This picture looks at the loop end-on. Using the right-hand rule, the field pushes the left side, where current comes out of the page, upward, and pushes the right side, where current goes into the page, downward. Equal and opposite pushes on opposite sides make the loop rotate clockwise, just like pushing up on the left side of a steering wheel and down on the right. That’s the magnetic force on a current from the last two lessons, put to work.

Keeping It Spinning

Split ring flips current every half turn
So the loop keeps turning one way
More loops + iron core: more power

A split ring commutator: a copper ring cut into two halves with gaps at the top and bottom. Two gray brushes touch the left and right sides of the ring and connect by wires to a battery below.

After half a turn, the sides of the loop have swapped places, and if nothing changed, the forces would push it back the other way. A split ring commutator fixes this. The ends of the loop connect to two halves of a ring, and brushes connect the ring to the battery. Every half turn, each brush slides onto the other half of the ring, which reverses the current in the loop, so the forces keep turning it the same direction. Real motors use many loops wound on an iron core to make the forces bigger.

Generators

Spin a coil in a magnetic field
The flux through it keeps changing
Induction makes a current

End-on view of a wire loop between a north pole on the left and a south pole on the right, tilted at an angle. A curved black arrow shows the loop being turned. Caption: a turning loop has changing flux, so current is induced.

A generator is a motor run backward. Instead of feeding current in, you turn the coil with a crank, a turbine, or a wind blade. As the coil turns in the magnetic field, the number of field lines passing through it keeps changing: lots of flux when the coil faces the poles, zero flux when it is edge-on. That changing flux induces a voltage and a current, exactly as Faraday’s law predicts. The faster the coil spins, the faster the flux changes and the more voltage it makes.

Alternating Current

Current reverses every half turn
This is alternating current (AC)
US outlets: 60 cycles per second

A graph of generator voltage versus time shaped like a smooth wave. It rises to a positive peak, falls through zero to a negative peak, and repeats, with one full cycle labeled one turn.

As a generator’s coil turns, each side moves up through the field and then down through it, so the induced current flows one way for half a turn and the opposite way for the next half. The voltage rises and falls smoothly, making a wave. Current that keeps reversing like this is called alternating current, or AC. Power plants in the United States make AC that completes 60 cycles every second (60 Hz). A battery, by contrast, makes direct current (DC), which flows only one way.

Same Parts, Opposite Jobs

Motor: electrical energy → motion (magnetic force on a current)
Generator: motion → electrical energy (electromagnetic induction)

Two cards side by side. Motor: electrical energy in, motion out, uses the magnetic force on a current. Generator: motion in, electrical energy out, uses induction. A note below says both are a coil of wire turning in a magnetic field.

A motor and a generator are built from the same parts: a coil of wire that can turn inside a magnetic field. The difference is which way the energy flows. A motor takes in electrical energy and puts out motion, using the magnetic force on a current. A generator takes in motion and puts out electrical energy, using electromagnetic induction. In fact, many electric and hybrid cars use their motors as generators when braking, turning the car’s kinetic energy back into electrical energy to recharge the battery.

Transformers

V_s / V_p = N_s / N_p

V_p and V_s = voltages across the primary (input) and secondary (output) coils, in volts (V)
N_p and N_s = number of turns on the primary and secondary coils

A square iron core. The primary coil on the left leg has 4 turns, with input voltage V p. The secondary coil on the right leg has 8 turns, with output voltage V s. Caption: more turns on the secondary means a higher voltage, a step-up transformer.

A transformer is two coils wrapped on the same iron core. Alternating current in the primary coil makes a changing magnetic field, and the iron carries that changing field through the secondary coil, where it induces a voltage. The voltage ratio equals the turns ratio. If the secondary has more turns, the voltage goes up (a step-up transformer). If it has fewer turns, the voltage goes down (a step-down transformer). Transformers only work with AC, because a steady DC current makes a field that doesn’t change, and no change means no induction.

From Power Plant to Home

A turbine spins a generator
Step up: high voltage, low current
Step down: safe voltage at home

A flow chart of four cards connected by downward arrows: power plant, where a turbine spins a generator; step-up transformer, to hundreds of thousands of volts; power lines, where high voltage means low current and less energy lost as heat; and step-down transformer, to 120 volts for your home.

In most power plants, steam, falling water, or wind spins a turbine, which turns a generator. Next, a step-up transformer raises the voltage to hundreds of thousands of volts. Since power is P = IV, raising the voltage lets the same power travel with much less current, and less current means much less energy wasted as heat in the long power lines. Near your neighborhood, step-down transformers lower the voltage to a safe 120 V for your outlets.

Worked Examples

Try each problem on your own first, then check your work against the solution.

Example 1: Which Way Does It Turn?

A motor loop is shown end-on between N and S poles. The left wire carries current into the page and the right wire carries current out of the page. Find the force on each side. Which way does the loop turn?

End-on view of a wire loop between a north pole on the left and a south pole on the right, with blue field lines pointing right. The left wire shows a cross for current into the page and the right wire shows a dot for current out of the page.

Field: The field points from N to S, to the right.
Left side: Current into the page. Right-hand rule: fingers right (B), thumb into the page (I), palm faces down. The force is down.
Right side: Current out of the page. Fingers right, thumb out of the page, palm faces up. The force is up.
Answer: Left side pushed down, right side pushed up, so the loop turns counterclockwise.

Compare this with the Electric Motors slide: reversing the current reversed the direction the motor spins. That’s how a cordless drill switches between forward and reverse.

Example 2: Step-Down Transformer

A phone charger’s transformer has 600 turns on its primary coil, which plugs into a 120 V outlet. Its secondary coil has 30 turns. What is the output voltage?

Knowns: N_p = 600, V_p = 120 V, N_s = 30
Equation: V_s/V_p = N_s/N_p, so V_s = V_p × N_s/N_p
Substitute: V_s = (120 V)(30/600) = (120 V)(0.050)
Answer: V_s = 6.0 V

The secondary has 1/20 as many turns, so the voltage drops to 1/20 of 120 V. That’s a step-down transformer.

Example 3: Step-Up Transformer

A power plant’s generator produces 12,000 V. A step-up transformer with 200 turns on its primary must raise this to 240,000 V. How many turns does the secondary need?

Knowns: V_p = 12,000 V, N_p = 200, V_s = 240,000 V
Equation: V_s/V_p = N_s/N_p, so N_s = N_p × V_s/V_p
Substitute: N_s = (200)(240,000 V / 12,000 V) = (200)(20)
Answer: N_s = 4,000 turns

Example 4: Why High Voltage?

A power plant sends 6.0 × 10⁵ W down a power line. Find the current in the line if the power is sent at 12,000 V, and again if it is sent at 240,000 V.

Knowns: P = 6.0 × 10⁵ W, V = 12,000 V or 240,000 V
Equation: P = IV, so I = P/V
At 12,000 V: I = (6.0 × 10⁵ W)/(12,000 V) = 50. A
At 240,000 V: I = (6.0 × 10⁵ W)/(240,000 V) = 2.5 A

Stepping the voltage up 20 times cuts the current to 1/20. Because the heat wasted in the wires grows with the current, sending power at high voltage saves a huge amount of energy.

Big Ideas

Motor: electrical energy → motion (magnetic force)
Generator: motion → electrical energy (induction)
Generators make AC; transformers change its voltage
V_s/V_p = N_s/N_p; high voltage means less loss

Back to the essential question: a motor turns electricity into motion because a magnetic field pushes on the current in a coil and makes it spin. A generator does the opposite: spinning a coil in a magnetic field changes the flux through it and induces a current. They use the same parts with the energy flowing in opposite directions, and transformers adjust the voltage so power plants can send that electricity to your home. This wraps up our electromagnetism unit.