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Question : 25
Total: 27
SECTION -D
(a) In a series LCR circuit connected across an ac source of variable frequency, obtain the expression for its impedance and draw a plot showing its variation with frequency of the ac source.
(b) What is the phase difference between the voltages across inductor and the capacitor at resonance in the LCR circuit?
(c) When an inductor is connected to
OR
(a) Draw the diagram of a device which is used to decrease high ac voltage into a low ac voltage and state its working principle. Write four sources of energy loss in this device.
(b) A small town with a demand of
Solution:
(a) Derivation of the expression for impedance 2 Plot of impedance with frequency
(b) Phase difference between voltage across inductor and capacitor
(c) Reason and calculation of self induction
(a)|
| = V m
| V R | = V R m
| V L | = V L m
From the figure, the pythagoras theorem gives
V m 2 = V R m 2 + ( V L m − V C m ) 2
V R m = i m R , V L m = i m X L , V C m = i m X C
V m = i m Z
( V m ) 2 = ( i m Z ) 2 = ( i m R ) 2 + ( i m X L − i m X C )
or,Z 2 = R 2 + ( X L − X C ) 2
Z = √ R 2 + ( X L − X C ) 2
[Note: award these two marks, If a student does it correctly for the other case i.e.,( V C > V D ) ]
180 ∘
(c) Inductor will offer an additional impedance toa c
R =
=
= 200 Ω
Impedance of the inductor
Z =
=
= 400 Ω
Since,Z = √ R 2 + ( X L ) 2
∴ ( 400 ) 2 − ( 200 ) 2 = ( X L ) 2
X L = √ 600 × 200 = 346.4 Ω
Inductance( L ) =
=
= 1.1 H
OR
(a)
Four sources of energy loss:
(i) Flux leakage between primary and secondary windings.
(ii) Resistance of the windings.
(iii) Production of eddy currents in the iron core.
(iv) Magnetization of the core.
(b) Total resistance of the line
= length × resistance per unit length
= 40 km × 0.5 Ω ∕ km
= 20 Ω
Current flowing in the lineI =
I =
= 300 A
Line loss in the form of heat
P = I 2 R
= ( 300 ) 2 × 20
= 1800 kW
(b) Phase difference between voltage across inductor and capacitor
(c) Reason and calculation of self induction
(a)
From the figure, the pythagoras theorem gives
or,
[Note: award these two marks, If a student does it correctly for the other case i.e.,
(b) Phase difference between voltage across inductor and the capacitor at resonance is
(c) Inductor will offer an additional impedance to
Impedance of the inductor
Since,
Inductance
OR
(a)
Working Principle: When the alternating voltage is applied to the primary, the resulting current produces an alternating magnetic flux in secondary and induces an emf in it. It works on the principle of mutual induction.
Four sources of energy loss:
(i) Flux leakage between primary and secondary windings.
(ii) Resistance of the windings.
(iii) Production of eddy currents in the iron core.
(iv) Magnetization of the core.
(b) Total resistance of the line
Current flowing in the line
Line loss in the form of heat
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