For a sinusoidal alternating current, if the maximum power is given, how do we calculate the mean power?
mean power = 1/2 x maximum power
The mean value of an alternating current is zero. Explain why heating occurs when there is an alternating current in a resistor.
Power = (I squared) x R
(I squared) is always positive.
Hence, power is always positive.
The mean value of an alternating current is zero. Explain why heating occurs when there is an alternating current in a resistor.
Power = (I squared) x R
( I squared) is always positive.
Hence, power is always positive.
Formula for maximum power in terms of peak current.
maximum power = (peak current squared) x R
Formula for maximum power in terms of peak voltage.
maximum power = (peak voltage squared)/R
Root-mean-square (r.m.s.) value of an alternating current
The value of the direct current that produces the same power (or same heating effect) in a resistor as the alternating current.
Root-mean-square value of an alternating voltage
The value of the direct voltage that produces the same power (or same heating effect) in a resistor as the alternating voltage.
Formula to calculate r.m.s. current using peak current.
r.m.s. current
= (peak current)/(square root of 2)
Formula to calculate r.m.s. voltage using peak voltage.
r.m.s. voltage
= (peak voltage)/(square root of 2)
A domestic supply voltage is stated as
240 V. Is 240 V the peak voltage or r.m.s. voltage?
r.m.s. voltage
A domestic supply voltage is stated as
240 V.
Is 240 V the peak voltage or r.m.s. voltage?
r.m.s. voltage
Describe the principle of operation of a simple iron-cored transformer.
- The alternating current in the primary coil is always changing. This results in an alternating magnetic flux in the soft iron core that is in phase with the current in the primary coil.
- The magnetic flux links with the secondary coil.
- Since there is a change in magnetic flux linkage with the secondary coil, an alternating e.m.f.is induced in the secondary coil (Faraday’s law of electromagnetic induction).
- This induced e.m.f. will be alternating at the same frequency as the current in the primary coil.
Why is the core of a transformer a continuous loop?
To concentrate the magnetic flux. This reduces the loss of magnetic flux.
Why is thermal energy generated in the core of a transformer?
The magnetic flux in the core is changing. Hence, an e.m.f is induced in the core. When eddy currents flow in the core, energy is dissipated as heat.
In a transformer, why is the core laminated?
To reduce the eddy current in the core. This reduces the energy lost in the core.
In a transformer, why is there less eddy current in a laminated core?
Because the core is made from thin strips of soft iron which are electrically insulated from one another.
Explain why a transformer will not operate using a direct current input.
According to Faraday’s law of electromagnetic induction, the e.m.f. induced is proportional to the rate of change of magnetic flux linkage. An e.m.f. is induced only when the magnetic flux is changing. A direct current has a constant magnetic flux.
Explain why the input potential difference and the output e.m.f of a transformer are not in phase.
Lenz’s law states that the direction of the induced e.m.f produces effects which oppose the change causing the e.m.f.
The current induced in the secondary coil produces a magnetic field which opposes the magnetic field produced in the primary coil.
Hence, the e.m.f.s are not in phase.
What is meant by an ideal transformer?
A transformer which is 100% efficient.
Input power = Output power
primary V x primary I
= secondary V x secondary I
For a transformer, give the equation which involves the ratios of N, V and I.
____ = ____ = ____
See notes.
What is the function of a transformer?
To step up and step down voltages.
In practice, a transformer will not be 100% efficient due to power losses.
List 4 sources of power losses in a transformer.
- Loss of magnetic flux between the primary and secondary coils.
- Resistive heating in the primary and secondary coils.
- Heating in the core due to eddy currents.
- Heating of the core due to repeated magnetisation and demagnetisation.
Why is electrical energy transmitted using alternating voltages?
- Alternating voltages can be stepped up or stepped down using a transformer.
- Transformers only work with a.c.
Why is electrical energy transmitted at high voltages?
P = VI
For the same power, transmitting at higher voltages means the current is smaller.
Power loss in cables = (I squared)R
The smaller the current, the less power is dissipated/lost in the transmission cables.
