11.2 Power Generation & Transmission

Bicycles can be fitted with a type of light powered by a dynamo in which a coil of wires is rotated by the motion of the pedals. A dynamo outputs direct current by using a split-ring commutator.

Before the split-ring commutator is fitted to the generator, it is tested by the manufacturer at a particular frequency. The variation in the current of the AC generator at a particular frequency is given by 

The rms value of the alternating current is 2.12 A.

Sketch a graph to show the variation of current against time

For each graph, label the peak current, I₀, with a numerical value.

For another bike light which only operates on direct potential difference, it is not possible to fit a split-ring commutator to the generator.

Suggest an alternative configuration for supplying the light with direct potential difference from an AC generator, such that the light shines continuously. Explain your reasoning.

Some bicycle lights rapidly flash off and on at a constant rate to make the cyclist more visible on the road. 

Describe and explain the configuration which would lead to this discontinuous flashing effect. You may sketch a graph to aid your explanation.

Root mean square (rms) values are used throughout this question.

A step down transformer connects an AC supply to a 18V system of 8 light up garden gnomes connected in parallel. The AC supply has a potential difference of 230V. Each gnome is rated at 35 W at average brightness.

Calculate the current in the primary coil of the transformer. Assume that the transformer is ideal.

Flux leakage is one reason why a transformer may not be ideal. 

Transformers are also used to supply electricity to homes with minimal power loss. A power company are evaluating a step-up transformer between a generator in a power plant and power cables leading to homes.

The primary coil has 300 turns and the secondary coil has 6000 turns and the cables in the primary and secondary coils have the same resistance.

Assuming the transformer is ideal, calculate the power loss in the secondary coil as a percentage of the power loss in the primary coil.

In a nuclear plant, steam heated by fission chain reactions rotates a turbine. This turbine then spins a generator, which is specified as "240 V_rms, 50 Hz AC". The generator produces an rms current of 6.00 A. 

An ideal transformer steps up the voltage to 2700 V_rms, in preparation for long-distance transfer through an aluminium power line with a resistivity of 2.65 × 10⁻⁸ Ω m.

Sketch two waveforms of the supply voltage on the same axes, one before and one after the transformer. Include numerical values on the axes where appropriate. 

In reality, transformers are not ideal and some power is lost.

Calculate the power lost over 5 km of the power cable which has a radius of 4 cm.

This cable connects to a step-down generator. The secondary coil supplies power to a flood lamp lighting an important game of ultimate frisbee. It is crucial that the lights do not flicker, but they have been fitted with a single diode. 

The lamps have been fitted with a single diode as they only operate with direct current: 

A step-up transformer has a peak current of 1.70 A and 500 turns in its primary coil and 1200 turns on the secondary coil. 

Calculate the value of the rms current output by the secondary coil for an 80% efficient transformer. 

A step-down generator on the other side of the cable brings the rms value of the alternating voltage to 230 V. This is supplied to the main electricity plugs inside a local library. A student charges their laptop. 

Outline how, and explain why, the alternating current from the mains source must be altered before it can charge a device.

The expression  represents the sinusoidal alternating voltage for an overhead cable on an electrical distribution system

Describe how such high voltages are obtained in practice.

A transformer is connected to an alternating power supply.

The transformer has 250 turns in the primary coil and 3500 turns in the secondary coil. The peak value of the voltage of the ac supply is 220 V.

Determine the root mean square (rms) value of the output voltage.

Describe the use of transformers in electrical power distribution.

A different transformer is used to transmit power to a village.

The transmission cables connecting the power station to the transformer have a total resistance of 3.5 Ω. The transformer is 92% efficient and steps down the voltage to 220 V. At the time of maximum power demand the effective combined resistance of the cables to the village and the village is 50 mΩ.

Calculate the current in the cables connected to the village.

Calculate the power supplied to the transformer.

Electrical power is produced for the national electricity grid using a series of alternating current (ac) generators connected to identical transformers.

The following data are available for one transformer. All values are root mean squares (rms).

Calculate the current output by this transformer to the grid.

Transformers are often used to step up voltage to 330 kV so that energy can be delivered across long distances.

State and explain the main advantage of using this very high potential difference.

The rms of the transmitted voltage is stepped down from 330 kV to 230 V to be used in the home.

Current from ac generators must be converted to dc current for some uses.

Complete the sketch to show an arrangement of diodes which would achieve full rectification with dc current in the load in the direction shown.

An ac voltage is established at the ends of a 75 Ω resistor. The graph shows the variation with time of the power dissipated in the resistor.

Find the rms value of the current.

Calculate the rms value of the voltage.

The coil is rotating with a frequency of 50 Hz.

Determine the times on the graph at points A, B, C and D.

A transformer has 700 turns in its primary coil and 300 in the secondary coil. An ac voltage of 220 V and frequency 50 Hz is established in the primary coil.

For the secondary coil calculate the induced

An investigation into rectification used the circuit shown.

For this investigation, sketch the resulting graph.

The investigation continues, using a second circuit.

Sketch the expected graph of the output voltage for this circuit.

A bridge rectifier consisting of four ideal diodes is connected to an ac generator with terminals X and Y.

Identify which diodes are conducting when terminal X of the ac generator is negative.

The graph shows the output from an ac generator after undergoing half-wave rectification.

The load resistor has a resistance of 3.6 kΩ. Capacitors of 360 nF and 60 µF are available.

Select the appropriate capacitor to smooth this output.