CBSE Class 12 · 2018 · Alternating CurrentLong Answer

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Electrical energy is transmitted over long distances from a power generating station to a city in the form of alternating current (a.c.) raised to a high voltage; at the receiving end the voltage is reduced to operate the devices, and as a result the power loss is reduced.
(a) Name the device used to change the alternating voltage to a higher or lower value, and state one cause of power dissipation in this device.
(b) Explain, with an example, how the power loss is reduced if the energy is transmitted over long distances as an alternating current rather than a direct current.

Solution

(a) The device is the transformer. One cause of power dissipation in it is Joule (

I^{2} R

) heating in the copper windings (other causes are eddy-current, hysteresis and flux-leakage losses).
(b) For a power

P

delivered at line voltage

V

through a line of resistance

R_{ℓ}

, the current is

I = \frac{P}{V}

and the heat lost in the line is

P_{l oss} = I^{2} R_{ℓ} = \frac{P ^{2} R _{ℓ}}{V ^{2}} \Rightarrow P_{l oss} \propto \frac{1}{V ^{2}}

Stepping the a.c. up to a high transmission voltage makes

I

small, so the

I^{2} R_{ℓ}

loss is greatly reduced; for example, raising the voltage tenfold cuts the current to one-tenth and the line loss to one-hundredth. A direct voltage cannot be changed by a transformer, so this economy is not available for d.c.

CBSE Class 12 Board · 2018 · Subjective

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CBSE Class 12 · 2018 · Alternating CurrentLong Answer

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