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Wize University Physics Textbook (Master) > Magnetic Induction

Transformers

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Transformers


The electricity that powers our homes is produced at industrial power generation sites and must be transported to us. This mechanism, along with many other applications, is enabled by transformers.
  • A transformer can be modelled as an iron core with two sets of coil windings: the primary coils (input) and the secondary coils (output).
  • The primary coils are wrapped around the core NpN_p times.
  • The secondary coils are wrapped around the core NsN_s times.
  • We assume the core has constant cross-sectional area and that all magnetic flux is preserved throughout the core.
  • Therefore, the change in magnetic flux is equal for both sets of coils.
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  • Faraday's Law for one set of coils gives V=−NΔΦmΔtV=-N\frac{\Delta\Phi_m}{\Delta t}.
  • Since the flux is equal, we can relate the induced voltage through the two sets of coils:
VpVs=NpNs\boxed{\frac{V_p}{V_s}=\frac{N_p}{N_s}}

Wize Concept
A transformer that causes an increase in voltage from input to output is called a step-up transformer. Likewise, a transformer that causes a decrease in voltage from input to output is called a step-down transformer.

  • The total electrical power input to the transformer equals the total electrical power output from the transformer.
  • Using the equation P=IVP=IV, we can also relate the induced current through the coils:
IsIp=NpNs\boxed{\frac{I_s}{I_p}=\frac{N_p}{N_s}}
Watch Out!
For the transformer equation with currents, the primary and secondary currents are flipped!

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Example: Transformers


Typically, power converted at a power plant is transformed to extremely high voltages for more efficient energy transmissions, and then stepped down to useable levels closer to the destination.

Consider a power plant where electricity is produced at 5.0 kilovolts. It is desired to step up this voltage to 800 kilovolts for transmission.

a) Using a standard transformer, what would be the ratio of primary coil turns to secondary coil turns for this step-up transformer?
b) If this higher voltage was to be stepped down all at once to 200 V, and there are only 10 secondary coil turns, how many primary coil turns must there be on the step-down transformer?

Part a)

We simply plug the given voltages into the transformer equation:
VpVs=NpNs5000 V800000 V=NpNsNpNs=1160\begin{aligned} \frac{V_p}{V_s}&=\frac{N_p}{N_s}\\ \frac{5000~V}{800000~V}&=\frac{N_p}{N_s}\\ \frac{N_p}{N_s}&=\frac{1}{160}\\ \end{aligned}
So for every 1 primary coil turn, there must be 160 secondary coil turns.

Part b)

To step-down from 800 kilovolts to 200 volts with 10 secondary coil turns, we plug values into the same equation (note, the "secondary" values from before are now "primary"):
VpVs=NpNs800000200=Np10Np=40000\begin{aligned} \frac{V_p}{V_s}&=\frac{N_p}{N_s}\\ \frac{800000}{200}&=\frac{N_p}{10}\\ N_p&=40000\\ \end{aligned}
Note - in real life, this would usually be done by two or more separate step-down transformers - having 10 coil turns on one side and 40,000 on the other would not be an ideal engineering arrangement.