CBSE Class 12 · 2019 · Alternating CurrentLong Answer

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(a) Draw the diagram of a device which is used to decrease a high a.c. voltage into a low a.c. voltage and state its working principle. Write four sources of energy loss in this device. (b) A small town with a demand of 1200 kW of electric power at 220 V is situated 20 km away from an electric plant generating power at 440 V. The resistance of the two-wire line carrying power is

0.5 Ω

per km. The town gets the power from the line through a 4000–220 V step-down transformer at a sub-station in the town. Estimate the line power loss in the form of heat.

Solution

(a) The device is a step-down transformer (

N_{s} < N_{p}

), working on mutual induction: a changing flux produced by the primary induces a (smaller) emf in the secondary. Four sources of energy loss are copper (

I^{2} R

) loss in the windings, eddy-current loss in the core, hysteresis loss in the core, and flux-leakage loss.
(b) Total line resistance (two wires, 20 km each way):

R = (20 + 20) \times 0.5 = 20 Ω

The line is fed at the sub-station input voltage

4000

V, so the line current is

I = \frac{P}{V} = \frac{1200 \times 1 0 ^{3}}{4000} = 300 A

Line power loss as heat:

P_{l oss} = I^{2} R = (300)^{2} \times 20 = 1.8 \times 1 0^{6} W = 1800 kW

P_{l oss} = 1800 kW

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CBSE Class 12 · 2019 · Alternating CurrentLong Answer

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