CDS (I) 2023 General Knowledge · Question 45 of 120

Correct — B, 220 V. The Indian domestic mains is an alternating supply, so its voltage swings continuously from positive to negative and back fifty times a second. A single number can only describe it if we agree which number, and by convention the figure quoted is the root mean square value — the steady direct voltage that would deliver the same average power to the same resistor. NCERT's Class 12 physics text puts the number and the convention together: 'It is customary to measure and specify rms values for ac quantities. For example, the household line voltage of 220 V is an rms value with a peak voltage of vm = √2 V = (1.414)(220 V) = 311 V.' So the reading between the live wire and the neutral wire in an Indian house is 220 V in root mean square terms, while the instantaneous voltage actually rises to about 311 V twice in every cycle. The colours in the stem follow the older Indian code, which UPSC has tested directly elsewhere — red for the live wire, black for the neutral and green for the earth.

• (a)160 V — Well below the supply. An appliance rated for the mains would run far under its rated power at this voltage, and incandescent lamps would visibly dim.
• (c)300 V — Close to the peak value rather than the root mean square value. The peak is about 311 V, so this option is what a candidate lands on by quoting the wrong one of the two numbers.
• (d)410 V — Roughly the three-phase line-to-line voltage of the Indian supply, not the line-to-neutral voltage a domestic socket delivers.

In an alternating supply both current and voltage vary sinusoidally with time, so their average over a full cycle is zero and useless as a description. The root mean square value is defined instead by squaring the waveform, averaging, and taking the square root, which gives the equivalent direct value for power purposes. For a sine wave the peak is √2 times the root mean square value. The Indian supply runs at 50 hertz.

Nothing about this question needs recall beyond one number, but it is worth knowing why three numbers float around it. The 220 V is the root mean square value quoted in textbooks; about 311 V is the peak the waveform actually reaches; and about 415 V is the line-to-line voltage in a three-phase supply, which is why the highest option is not random. One present-day nuance worth carrying: the declared standard single-phase supply voltage in India is 230 V with a tolerance band, so the modern nameplate on many appliances reads 230 V rather than 220 V. The options in this paper leave no ambiguity — the nearest alternatives are 160 V and 300 V — but a candidate who has seen 230 V should know why both figures are in circulation.

• The household line voltage of 220 V is a root mean square value; the corresponding peak is about 311 V.
• For a sinusoidal waveform, peak equals √2 times the root mean square value, a factor of about 1.414.
• The Indian domestic supply alternates at 50 hertz.
• In the older Indian colour code the live wire is red, the neutral black and the earth green.
• About 415 V is the three-phase line-to-line voltage, which is why an option near 410 V appears in the paper.

• Quoting the peak value when the question asks for the root mean square value, or the reverse.
• Confusing the line-to-neutral voltage of a domestic socket with the line-to-line voltage of a three-phase supply.
• Assuming the earth wire carries the supply; it is a safety path and normally carries no current.

As a straight recall of the supply voltage or frequency, as a peak-against-root-mean-square conversion, or as a colour-code item on domestic wiring.

• practice — not a real PYQ

  The peak value of the voltage in an Indian domestic supply quoted as 220 V is approximately

  • (a)220 V
  • (b)156 V
  • (c)311 V
  • (d)440 V

  Answer(c) 311 V — for a sine wave the peak is √2 times the root mean square value, and 1.414 multiplied by 220 gives about 311.

• practice — not a real PYQ

  The frequency of the alternating current supplied to Indian households is

  • (a)25 hertz
  • (b)50 hertz
  • (c)60 hertz
  • (d)100 hertz

  Answer(b) 50 hertz — the Indian supply completes fifty cycles a second, so the direction of the current reverses a hundred times each second.