SATHEE: alternating-currents Question 37

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Question: Q. 2. (a) State the principle of working of a transformer.

(b) Define efficiency of a transformer.

(d) Calculate the current drawn by the primary of a $90$ efficient transformer which steps down $220 V$ to $22 V$ , if the output resistance is $440 Ω$ .

U] [CBSE Comptt. I, II, III 2018]

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Solution:

Ans. (a) Principle of working

(b) Defining efficiency

(d) Calculating the current drawn

$1 / 2 + 1 / 2$

(a) A tansformer works on the principle of mutual induction.

(Alternatively-an emf is induced in the secondary coil when the magnetic flux, linked with it changes with time due to a (time) changing magnetic flux linked with the primary coil).

(b) The efficiency of a transformer equals the ratio of the output power to the input power.

Alternatively

Efficiency $= \frac{output power}{inputpower}$

$Efficiency = \frac{V_{s} I_{s}}{V_{p} I_{p}}$

(ii) joule heat losses

(iii) hysteresis losses

(iv) magnetic flux leakage losses

(Any two)

(d) We have

$\begin{aligned} \frac{V_{s} I_{s}}{V_{p} I_{p}} & = 90 & ∴ \frac{22 I_{s}}{220 I_{p}} & = 0.9 & or \frac{I_{s}}{I_{p}} & = \frac{0.9}{0.1} = 9 ∴ & I_{p} & = \frac{I_{s}}{9} = \frac{(\frac{22}{440})}{9} A & = \frac{1}{180} A & = 0.0056 A \end{aligned}$

[CBSE Marking Scheme, 2018]

(AI Q. 3. (i) Draw a labelled diagram of an $a c$ generator. Obtain the expression for the emf induced in the rotating coil of $N$ turns each of cross-sectional area $A$ , in the presence of a magnetic field $\vec{B}$ .

(ii) A horizontal conducting rod $10 m$ long extending from east to west is falling with a speed $5.0 {ms}^{- 1}$ at right angles to the horizontal component of the Earth’s magnetic field, $0.3 \times 10^{- 4} Wb m^{- 2}$ . Find the instantaneous value of the emf induced in the rod. U [O.D. Set III 2017]