Please provide a rating, it takes seconds and helps us to keep this resource free for all to use
In addition to the revision notes for Power in an Alternating Circuit. Transformers on this page, you can also access the following Magnetism learning resources for Power in an Alternating Circuit. Transformers
| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
|---|---|---|---|---|---|---|
| 16.17 | Power in an Alternating Circuit. Transformers |
In these revision notes for Power in an Alternating Circuit. Transformers, we cover the following key points:
Electric power delivered by a source is the rate of energy consumption, i.e.
In DC circuits, quantities such as current, potential difference and electromotive force are constant with time, so the efficiency of circuit (the part of the total energy converted in the desired form, i.e. as useful energy) is calculated by
In AC circuits however, the discussion about electrical power is more complicated as both current and voltage in circuit are not constant; they both vary in a sinusoidal fashion. Thus, we can write
where R is the resistance of the AC circuit.
Since the current in an AC circuit as a function of time, is
we obtain for the power dissipated in such a circuit:
or
We can use the concept of average power to make the things easier. For this, we must write the rms current instead of the maximum current in the above formula. In this way, we obtain for the average power in an AC circuit
= irms2 ∙ R = (imax/√2)2 ∙ R = imax2 ∙ R/2 = Pmax/2
If we consider all three quantities responsible for the impedance in the circuit, we obtain for the rms current
We can express the average power delivered in the circuit as
= εrms/Z ∙ irms ∙ R = εrms ∙ irms ∙ R/Z
The quantity R/Z is the cosine of the phase constant φ discussed in the previous tutorial, i.e.
Hence, combining the last two equations, yields
= εrms ∙ irms ∙ cosφ
The 'cos φ' term is called "power factor." It is independent from the sign of the phase constant φ because cos φ = cos (-φ) for every value of φ.
The value of power factor is very important in maximizing the rate of energy supplied to a resistive load. To achieve this, the value of power factor must be as close to 1 as possible. This means the phase constant must be as close as possible to zero, i.e. the values of inductive and capacitive load must be very close to each other. If a circuit is more inductive than capacitive, we increase the capacitance in the circuit to balance the reactances. On the other hand, if the circuit is more capacitive than inductive, we decrease the capacitance by connecting an extra capacitor in the circuit.
Transformers are passive electric devices used to change the value of voltage in a circuit. Transformers use electromagnetic induction to transport electricity.
Power stations produce large amounts of energy in the unit time. Typical values range from hundreds of megawatt hour (MWh) to several gigawatt hour (GWh) of electricity. To carry this huge amount of energy throughout the transportation system, we can use two methods:
The second method is more convenient as it reduces the energy loss during transportation. Therefore, we must increase the value of voltage during the way and then decrease it near the end user premises to make the electricity useable. During this process, we use two types of electric transformers: step-up transformers, which are voltage increasers and step-down transformers, which are voltage reducers.
Electricity is usually generated at 11kV in power stations although the generation voltage may vary in the range between 11kV and 33kV. Then the voltage increases during transportation to 220kV, 400kV or 765kV depending on the country. Step-up transformers are installed at high voltage poles to achieve this. Then, the voltage decreases to 20kV near residential areas (in electric substations) using step-down transformers and then, the voltage decreases further to 110V or 220V in electric cabins (using again step-down transformers) depending on the country. This is the value of voltage used in most part of daily activities.
Step-up transformers have more turn in the secondary coil while step-down transformers have more turns in the primary coil. The alternating current flowing through the primary coil produces a variable magnetic flux in the core. Since the number of turns is different, the flux produced in the secondary coil changes, generating an induced emf in the secondary coil (in the primary coil the emf is due to the input source). However, the frequency of current (and voltage) doesn't change.
An ideal transformer has no any power loss during the induction from primary to secondary coil. However, this is practically impossible. Some of the energy (power) is lost during this process despite the coils are made of soft iron to reduce this loss. Hence, we can write
The efficiency of a transformer is:
For simplicity, we often consider ideal transformers to explain the related phenomena. In ideal transformers, we have
The relationship between the emf's and the number of turns in each coil is
where N1 and N2 are the numbers of turns in the primary and secondary coil respectively. The ratio N1/N2 is called the turns factor.
For ideal transformers, the emf's in each coil are equal to the corresponding voltages at their ends. Hence, we can write
Combining all the above equations, we obtain for an ideal transformer
This means the current is inversely proportional to electromotive force, voltage and number of turns in the transformer.
Enjoy the "Power in an Alternating Circuit. Transformers" revision notes? People who liked the "Power in an Alternating Circuit. Transformers" revision notes found the following resources useful:
Please provide a rating, it takes seconds and helps us to keep this resource free for all to use
We hope you found this Physics tutorial "Power in an Alternating Circuit. Transformers" useful. If you did it would be great if you could spare the time to rate this physics tutorial (simply click on the number of stars that match your assessment of this physics learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of physics and other disciplines.