Syllabus: Alternating currents, peak and RMS value of alternating current/voltage; reactance and impedance; LCR series circuit (phasors only), resonance, power in AC circuits, power factor, wattless current. AC generator, Transformer.
Numericals:
6. A power transmission line feeds input power at 2300 V to a step- down transformer with its primary windings having 4000 turns. What should be the number of turns in the secondary in order to get output power at 230 V?
5. 7.1: A 100 Ω resistor is connected to a 220 V, 50 Hz ac supply.
(a) What is the rms value of current in the circuit?
(b) What is the net power consumed over a full cycle?
4. 7.2: (a) The peak voltage of an ac supply is 300 V. What is the rms voltage?
(b) The rms value of current in an ac circuit is 10 A. What is the peak current?
3. Example 7.4 A 15.0 μF capacitor is connected to a 220 V, 50 Hz source. Find the capacitive reactance and the current (rms and peak) in the circuit.
If the frequency is doubled, what happens to the capacitive reactance and the current?
2. Example 7.2 : A pure inductor of 25.0 mH is connected to a source of 220 V. Find the inductive reactance and rms current in the circuit if the frequency of the source is 50 Hz.
1. Example 7.1 A light bulb is rated at 100W for a 220 V supply. Find
(a) the resistance of the bulb; (b) the peak voltage of the source; and
(c) the rms current through the bulb.
Questions:
28. Give the disadvantages of transmitting AC over long distances, at low voltage & high current?
27. Does a step-up transformer contradict the principle of conservation of energy?
26. Does a transformer change the frequency of an AC?
25. Which device will you use to step-up A.C voltage?
24. Mention four types of losses in a Transformer.
I) Copper or resistance Loss: Heat is produced due to the resistance of the copper windings of Primary and Secondary coils when current flows through them.
This can be avoided by using thick wires for winding.
II) Flux Loss: In actual transformer coupling between Primary and Secondary coil is not perfect. So, a certain amount of magnetic flux is wasted.
Linking can be maximised by winding the coils over one another.
III) Iron Losses:
a) Eddy Currents Losses:
When a changing magnetic flux is linked with the iron core, eddy currents are set up which in turn produce heat and energy is wasted.
Eddy currents are reduced by using laminated core instead of a solid iron block because in laminated core the eddy currents are confined within the lamination, as their paths are broken..
IV) Hysteresis Loss:
When alternating current is passed, the iron core is magnetised and demagnetised repeatedly over the cycles and some energy is lost in the process.
This can be minimised by using suitable material with thin hysteresis loop such as soft iron.
24. Can a transformer be used to step up or step-down D.C voltage?
23. What is meant by transformer ratio?
22. Write working and principle of a transformer. What are step up and step down transformers?
Transformer is a device which converts lower alternating voltage into higher alternating voltage at lower current and vise versa.
Principle:
Transformer is based on the phenomenon of Mutual Induction.
It is the phenomenon of inducing emf in the secondary coil due to change in current in the primary coil.
Construction:
Theory:
By Faraday's laws,
The emf induced across secondary coil, due to the mutual induction is ES = - NS dΦ / dt
And the emf induced across primary due to self induction is EP = - NP dΦ / dt
Flux is common through both the coils.
ES / EP = NS / NP = K
(where K is called Transformation Ratio or Turns Ratio)
For an ideal transformer,
Output Power = Input Power
ES.Is = Ep.Ip
ES / EP = IP / IS
ES / EP = IP / IS = NS / NP
Efficiency (η):
η = ES.Is / Ep.Ip
For an ideal transformer η is 100%
Step - up transformer
NS > NP i.e. K > 1
ES > EP & IS < IP
(Step - down transformer: reverse of the above)
21. Write working and principle of AC generator and find expression for the induced EMF across its armature.
20. What is the phase difference between AC current and voltage in LCR series circuit, at resonance?
19. Find expression for the average AC power consumed on one cycle.
19. What is wattless current? Give an example.
18. Find expression for the average AC power consumed on one cycle in pure (a) inductor (b) pure capacitor.
17. Draw the variation curve of peak current in LCR series circuit with the frequency of applied source.
16. Write mathematical expression for the impedance in LCR series circuit and hence find expression for resonant frequency.
15. What is electrical resonance in LCR series circuit. Give an example.
14. Using current and voltage phasors, find expression for the impedance in LCR series circuit.
13. Draw current and voltage phasors for (a) a pure capacitive and (b) pure inductive circuit when AC voltage is applied across it.
12. Write the value of phase difference in applied AC voltage and resulting AC current in an (a) inductor and (b) capacitor.
11. Draw graph showing variation of current and voltage in a pure inductor when AC voltage is applied across it.
10. Draw graph showing variation of current and voltage in a pure capacitor when AC voltage is applied across it.
9. How can you explain that an inductor offers very low reactance to a high frequency AC input signal?
8. Write the value of reactance when a DC voltage is applied across a capacitor.
7. Write expressions for inductive reactance and capacitive reactance. Draw curves to show how they very with the applied AC frequency.
6. Find expression for AC current in a pure inductor when an AC voltage is applied across it.
5. Find expression for AC current in a pure capacitor when an AC voltage is applied across it.
4. What is the average value of AC voltage over one cycle?
3. What is the average value of AC current over one cycle?
2. Find expressions for The RMS value of alternating current and voltage.
1. What is an alternating current. An AC voltage is applied across a registor, find expression for AC current in it.
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