23.7 Transformers

• This schematic shows the coil of a DC motor.
• The one driving the motor is represented as a variable emf.
• When the motor is not turning, back emf is zero.

• The generator output of a motor is proportional to the motor's speed.
• When the motor is first turned on, it's zero because the coil gets the full driving voltage and the motor draws the maximum current.
• As the motor turns faster and faster, the back emf grows, always opposing the driving emf, and reduces the voltage across the coil and the amount of current it draws.
• This effect can be seen in a number of situations.
• When a vacuum cleaner, refrigerator, or washing machine is first turned on, lights in the same circuit dim briefly due to the drop produced in feeder lines by the large current drawn by the motor.
• When a motor comes on, it draws more current than when it runs at its normal speed.
• When a mechanical load is placed on the motor, like an electric wheelchair going up a hill, the motor slows, the back emf drops, and more work can be done.
• If the motor runs at too low a speed, the larger current can cause it to heat up and even burn it out.
• If there is no mechanical load on the motor, it will increase its speed until the back emf is equal to the driving emf.
• The motor needs enough energy to work.

• The coils are driven by a 48.0 V emf.
• After being turned on, they draw a current and use it to transfer heat.
• If the back emf is 40.0 V, then the total voltage across the coil is 8.0 V (48.0 V minus the 40.0 V back emf), and the current drawn is.
• The power dissipated under normal load.
• The former 5.76 kW would burn out the coil if sustained, whereas the latter will not cause a problem for this motor.

• Less current is required for a given amount of power, and this means less line loss, because power is sent long distances at high voltages.
• Transformer are used to produce lower voltage at the user's location because of high voltages.

• The plug-in transformer is familiar with the proliferation of electronic devices that operate on voltages other than 120 V AC.
• Most are in the range of 3 to 12 V. The power distribution system has transformers.
• To limit energy losses, electric power is usually generated at greater than 10 kV and transmitted long distances at higher voltages.
• The local power distribution goes through a substation and is sent short distances at different voltages.
• For safety at the individual user site, this is reduced to 120, 240, or 480 V.

• The primary and secondary coils are used.
• In normal use, the input and output are put on the primary and secondary, respectively.
• The iron core traps the magnetic field created by the primary coil.
• Since the input voltage is AC, a time-varying magnetic flux is sent to the secondary, inducing its AC output voltage.

• A transformer has two coils wound on a ferromagnetic core that is laminated to minimize eddy currents.
• The magnetic field created by the primary is mostly confined to and increased by the core.

• If the coil resistance is small, you can assume that the output voltage is equal to the emf.
• Both sides of the coil have the same cross-sectional area and magnetic field strength.

• There is a subtle reason for this.
• The minus sign is an example of self-inductance, a topic to be explored in some detail in later sections.

• The loop rule tells us that the emf is equal to the input voltage.

• Depending on the ratio of the number of loops in the transformer's coil, the transformer's output voltage can be less than or equal to the input voltage.
• Some transformers give a variable output by allowing connection to be made at different points on the secondary coil.
• The electrical power output of a transformer equals its input if resistance is negligible.
• In practice, transformer efficiency often exceeds 99%.

• The output and input currents of a transformer are related.

• A portable x-ray unit has a step-up transformer that can be used to convert the 120 V input into the 100 kV output needed for the xray tube.
• The primary has 50 loops and draws a current.

• We enter the known values when we solve for the number of loops in the secondary.

• A large number of loops in the secondary is required to produce such a large voltage.
• It would be true for neon sign transformers and those that supply high voltage inside TVs and CRTs.

• We can find the output current of the secondary by entering known values.

• The current output is less than the input.
• In some 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.
• There is a power input here.
• The power output is the same as we assumed in the derivation of the equations used.

• It's clear why we can't use transformers to change DC voltages because they're based on the law of induction.
• If there is no change in the primary, there is no change in the secondary.
• It is possible to connect DC to the primary coil through a switch.
• AC is in use wherever it is necessary to increase or decrease voltages, because the secondary produces a voltage like that when the switch is open and closed.

• If the output is switched on and off as on the top graph, it will look like it is on the bottom graph.
• This is not what most AC appliances need.

• The batteries need a 15.0 V output to be charged.
• It has a step-down transformer and a 120 V input.

• The secondary should have a small number of loops.

• Solving for and entering known values can be used to get the current input.

• The number of loops in the secondary is small.
• A small input current can produce a larger output current in a step-down transformer.
• There are a small number of heavy loops in the secondary of transformers when they are used to operate large magnets.
• The secondary has low internal resistance and can produce large currents.
• This solution is based on the assumption of 100% efficiency, which is reasonable for good transformers.
• The Ni-Cd batteries need to be charged from a DC power source.
• The secondary coil needs to be converted into DC.
• This is done using a device called a rectifier, which is a device that allows only one-way flow of current.

• In Electrical Safety: Systems and Devices, transformer applications are discussed.