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Question : 24
Total: 26
SECTION - E
(i) Draw a labelled diagram of a step-down transformer. State the principle of its working.
(ii) Express the turn ratio in terms of voltages.
(iii) Find the ratio of primary and secondary currents in terms of turn ratio in an ideal transformer.
(iv) How much current is drawn by the primary of a transformer connected to
OR
(a) Explain the meaning of the term mutual inductance. Consider two concentric circular coils, one of radius
(b) A rectangular coil of area
Solution:
(i) Principle of working: It works on the principle of mutual induction i.e. if two coils are inductively coupled and when current or magnetic flux is changed through one of the two coils, then induced e.m.f. is produced in the other coil.
K =
=
A transformer with a primary winding of 1000 turns and secondary winding of 100 turns has a turns ratio of1000 : 100 10 : 1
(iii)E s I s = E p I p
(Input Power = Output Power)
⇒
=
⇒
=
= K
(iv)e p = 220 v ; e s = 110 v , e s I s = 550 W
Now,
e p I p = e s I s
I p =
=
= 2.5 A
OR
(a) Meaning of Mutual Inductance
Expression
(b) Proof
Diagram
(a) Mutual Inductance is the property of a pair of coils due to which an emf induced in one of the coils due to the change in the current in the other coil.
Mathematically e 2 =
∴ M = −
Let a currentI 2
B 2 =
∴ ϕ 1 = π r 2 B 2 =
I 2 = M 12 I 2
ThusM 12 =
I 2 = M 21
(b)
Flux at any time 't
ϕ B = B A cos θ = B A cos ω t
From Faraday's Law, induced emf
e = − N
= N B A
( cos ω t )
Thus the instantaneous value of emf is
E = N B A ω s i n ω t
For maximum value of emfs i n ω t = ± 1
i.e.,e 0 = N B A ω = 2 π f N B A
(ii) Turns ratio is
A transformer with a primary winding of 1000 turns and secondary winding of 100 turns has a turns ratio of
(iii)
(iv)
Now,
OR
(a) Meaning of Mutual Inductance
Expression
(b) Proof
Diagram
(a) Mutual Inductance is the property of a pair of coils due to which an emf induced in one of the coils due to the change in the current in the other coil.
Let a current
Thus
(b)
Flux at any time '
From Faraday's Law, induced emf
Thus the instantaneous value of emf is
For maximum value of emf
i.e.,
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