Solved problems for the chapter:

Rectification, Smoothing and Transformer

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Transformer

1. Voltage transformer

2. Power conversion - transformer efficiency

3. Current transformer

4. Forum

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Oscillator Circuit

1. Oscillating circuit current

1.1. Change in voltage with time

2. Oscillating circuit voltage

2.1. Change in current with time

3. Natural frequency of oscillation

4. Energy of an oscillating circuit

4.1. Electrical energy of the capacitor

4.2. Magnetic energy of the inductor

4.3. Total energy

5. Forum

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Alternating Voltage

1. Obtaining sinusoidal alternating voltage

2. Average power and effective voltage

3. Forum

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Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:rectification%2C_smoothing_and_transformer/4528/

Example 1.

A voltage with a peak value of is connected to the primary coil of a transformer having 1200 turns. How many turns should the secondary coil have if we want to reduce the voltage to ?

Example 2.

An alternating voltage with a peak value of 200 V and an average power of 14 kW is connected to the primary coil of a current transformer, which has 1300 turns. Calculate the number of turns of the secondary coil if we want to obtain a current with a peak value of 12 kA. We ignore the power losses in the transformer.

Calculate the oscillation period of an alternating current in a closed oscillator circuit consisting of a coil with an inductance of and a capacitor with a capacitance of .

Calculate the new natural frequency if the frequency of an oscillator circuit before immersion in oil with a relative permittivity of was equal to .

Calculate the relative permeability of a liquid if, by pouring it into the coil of an oscillating electric circuit, the natural frequency of the circuit increases by 0.05 %.

The electric oscillator circuit shown below consists of a coil with an inductance of and a capacitor with a capacitance of . We momentarily connect an 80 V voltage source to the oscillator circuit and turn it off.

At what frequency does the circuit oscillate?
What is the energy of the circuit?
What is the maximum current flowing through the circuit?

An oscillator circuit oscillates at a frequency of . The capacitance of the capacitor is .

What is the inductance of the coil in the circuit?
What is the peak value of the current through the coil if the peak value of the voltage across the capacitor is ?

A bridge rectifier using four ideal diodes is shown in the figure below.

The sinusoidal alternating electromotive force (e.m.f.) applied between points A and B has a root-mean-square (r.m.s.) value of .

- On the figure above, circle the diodes that conduct when point B is positive with respect to point A.
- Calculate the maximum potential difference across resistor R.
A capacitor is connected into the circuit to produce smoothing of the potential difference across resistor R. The variation with time of the potential difference across resistor R is shown in the graph below.
- On the figure above, draw the symbol for a capacitor, connected so as to produce smoothing.
- State the effect, if any, on the magnitude of the ripple on when, separately:
  - a capacitor of larger capacitance is used
  - the resistor R has a smaller resistance.

Calculate the inductance of a coil in a closed oscillator circuit in which there is a capacitor with a capacitance of and the natural frequency of the circuit is .

10.

A student is asked to design a circuit by which a direct voltage of peak value is obtained from a alternating supply. The student uses a transformer that may be considered to be ideal and a bridge rectifier incorporating four ideal diodes. The partially completed circuit diagram is shown in the figure below.

On the figure above, draw symbols for the four diodes so as to produce the polarity across the load as shown on the diagram.
Calculate the ratio

11.

A transformer is illustrated in the figure below.

Explain why the coils are wound on a core made of iron.
Suggest why thermal energy is generated in the core.

12.

The circuit for a full-wave rectifier using four ideal diodes is shown in the figure below.

A resistor R is connected across the output AB of the rectifier. On the figure above,

draw a circle around any diodes that conduct when the terminal X of the input is positive with respect to terminal Y,
label the positive (+) and the negative (–) terminals of the output AB.

13.

A simple transformer is illustrated in the figure below.

State
- why the iron core is laminated,
- what is meant by an ideal transformer.
An ideal transformer has 300 turns on the primary coil and 8100 turns on the secondary coil. The root-mean-square input voltage to the primary coil is . Calculate the peak voltage across the load resistor connected to the secondary coil.

14.

A bridge rectifier consists of four ideal diodes A, B, C and D, connected as shown in the figure below.

An alternating supply is applied between the terminals X and Y.

- On the figure above, label the positive (+) connection to the load resistor R.
- State which diodes are conducting when terminal Y of the supply is positive.
The variation with time of the potential difference across the load resistor R is shown in the graph below.

The load resistor R has resistance .
- Use the graph above to determine the mean power dissipated in the resistor R.
- On the figure above, draw the symbol for a capacitor, connected so as to increase the mean power dissipated in the resistor R.

15.

The output of an ideal transformer is connected to a bridge rectifier, as shown in the figure below.

The input to the transformer is and the maximum potential difference across the load resistor is .

On the figure above, mark with the letter P, the positive output from the rectifier.
Calculate the ratio

16.

A simple transformer with a soft-iron core is illustrated in the figure below.

Explain why the core is
- made of iron,
- laminated.
An e.m.f. is induced in the secondary coil of the transformer. Explain how a current in the primary coil gives rise to this induced e.m.f.

17.

A bridge rectifier contains four ideal diodes A, B, C and D, as shown in the figure below.

The output of the rectifier is connected to a load L of resistance .

On the figure above, mark with the letter P, the positive terminal of the load.
The variation with time of the potential difference across the input to the rectifier is shown in the graph below.

Calculate the root-mean-square (r.m.s.) current in the load L.
The potential difference across the load L is to be smoothed using a capacitor. On the figure above, draw the symbol for a capacitor, connected to produce smoothing.

18.

The components for a bridge rectifier are shown in the figure below.

Complete the circuit in the figure above by showing the connections of the supply and of the load to the diodes.
Suggest one advantage of the use of a bridge rectifier, rather than a single diode, for the rectification of alternating current.
State
- what is meant by smoothing
- the effect of the value of the capacitance of the smoothing capacitor in relation to smoothing.

19.

A simple transformer is illustrated in the figure below.

- State why the transformer has an iron core, rather than having no core.
- Explain why the core is laminated.
By reference to the action of a transformer, explain why the input to the transformer is an alternating voltage, rather than a constant voltage.

20.

A simple iron-cored transformer is illustrated in the figure below.

- State why the primary and secondary coils are wound on a core made of iron.
- Suggest why thermal energy is generated in the core when the transformer is in use.
The root-mean-square (r.m.s.) voltage and current in the primary coil are and respectively. The r.m.s. voltage and current in the secondary coil are and respectively.
- Explain, by reference to direct current, what is meant by the root-mean-square value of an alternating current.
- Show that, for an ideal transformer,

21.

An ideal transformer is illustrated in the figure below.

Explain why, when there is an alternating current in the primary coil, there is a current in the load resistor.

22.

A simple iron-cored transformer is illustrated in the figure below.

Suggest why the core is
- a continuous loop,
- laminated.
Use Faraday’s law to explain the operation of the transformer.
State two advantages of the use of alternating voltages for the transmission and use of electrical energy.

23.

A simple iron-cored transformer is illustrated in the figure below.

State one function of a transformer.
A sinusoidal alternating current in the primary coil gives rise to a varying magnetic flux linking the secondary coil. Use Faraday’s law to explain why the output from the transformer is an electromotive force (e.m.f.) that is alternating.
State why the soft-iron core of the transformer is laminated.

24.

An ideal transformer is shown in the figure below.

Explain
- why the core is made of iron,
- why an electromotive force (e.m.f.) is not induced at the output when a constant direct voltage is at the input.
An alternating voltage of peak value is applied across the 1200 turns of the primary coil. The variation with time of the e.m.f. induced across the secondary coil is shown in the graph below.

Use data from the graph above to
- calculate the number of turns of the secondary coil,
- state one time when the magnetic flux linking the secondary coil is a maximum.

25.

The figure below shows four diodes and a load resistor of resistance , connected in a circuit that is used to produce rectification of an alternating voltage.

- State what is meant by rectification.
- State the type of rectification produced by the circuit in the figure above.
A sinusoidal alternating voltage is applied across the input terminals X and Y. The variation with time of is given by the equation

where is in volts and is in seconds.
- On the figure above, label the output terminals P and Q with the appropriate symbols to indicate the polarity of the output voltage .
- The magnitude of the output voltage varies with as shown in the graph below.
  
  On the graph above, label both of the axes with the correct scales. Use the space below for any working that you need.
The output voltage in (b) is smoothed by adding a capacitor to the circuit in the figure above. The difference between the maximum and minimum values of the smoothed output voltage is of the peak voltage.
- On the figure above, draw the circuit symbol for a capacitor showing the capacitor correctly connected into the circuit.
- Calculate the capacitance of the capacitor.

26.

Four diodes are used in a bridge rectifier circuit to produce rectification of a sinusoidal a.c. input voltage . The figure below shows part of the circuit, but three of the diodes are missing.

The p.d. across the load resistor R is the output p.d. of the bridge rectifier.

- State the name of the type of rectification produced by a bridge rectifier.
- Complete the figure above by drawing the three missing diodes, correctly connected.
- On the figure above, draw an arrow to indicate the direction of the current in resistor R.
has amplitude and period . The graph below shows the variation with time of .
- On the graph below, sketch the variation of with between and .
- The power dissipated in the resistor is . On the graph below, sketch the variation of with between and .

27.

Part of an electric circuit is shown in the figure below.

The circuit is used to produce half-wave rectification of an alternating voltage of potential difference (p.d.) . The output p.d. across the resistor is .

- A component is missing from the circuit of the figure above. Complete the circuit diagram in the figure by adding the circuit symbol for the missing component, correctly connected.
- A capacitor C is shown in the circuit in the figure above. State the effect on of including the capacitor in the circuit.
The graph below shows the variation with time of .

The graph below shows the variation with of .
- Determine the frequency of .
- Show that the time constant for the discharge of the capacitor through the resistor is .
- Calculate the capacitance of . Give a unit with your answer.

28.

Alternating current (a.c.) is converted into direct current (d.c.) using a full-wave rectification circuit. Part of the diagram of this circuit is shown in the figure below.
- Complete the circuit in the figure above by adding the necessary components in the gaps.
- On the figure above mark with a + the positive output terminal of the rectifier.
The output voltage of an a.c. power supply varies sinusoidally with time as shown in the graph below.
- Determine the equation for in terms of , where is in volts and is in seconds.
- The supply is connected to a resistor. Calculate the mean power dissipated in the resistor.