The AC mains domestic supply current in India changes direction in every
- (a)50 s
- (b)1/50 s
- (c)100 s
- (d)1/100 s
Correct — D, 1/100 s. India's domestic mains is alternating current at a frequency of 50 Hz, so one complete cycle takes 1/50 s (0.02 s). In each cycle the current first flows one way and then the other, reversing at every zero-crossing — that is twice per cycle. Half of 1/50 s is 1/100 s, so the current changes direction every 1/100 s (100 times a second).
- (a)50 s — This confuses the frequency (50 Hz) with a time interval. 50 is the number of cycles per second, not the seconds between reversals; a 50-second reversal would be an almost-DC supply.
- (b)1/50 s — This is the full time period T of one complete cycle. The current reverses twice within a cycle, so the gap between successive reversals is half of this, i.e. 1/100 s, not 1/50 s.
- (c)100 s — Again it treats a rate (100 reversals per second) as if it were a duration. 100 seconds is not a mains time scale at all.
Alternating current periodically reverses its direction of flow. For a supply of frequency f, one complete cycle takes a time period T = 1/f. In a single cycle the current goes positive, returns to zero, goes negative and returns again — so it reverses direction twice per cycle, once at each zero-crossing. India's mains frequency is 50 Hz.
The trap is to stop at the time period T = 1/50 s. But the question asks how often the current changes direction, and that happens twice in each cycle, so the interval is half the period: (1/50)/2 = 1/100 s. Equivalently, the current reverses 100 times every second.
- Indian domestic AC mains: about 230 V at a frequency of 50 Hz.
- Time period of one cycle T = 1/frequency = 1/50 s = 0.02 s.
- AC reverses direction twice per cycle (at each zero-crossing), i.e. every T/2 = 1/100 s.
- So the current changes direction 100 times per second while completing 50 full cycles per second.
- Choosing 1/50 s (the full period) instead of half the period for a direction change.
- Treating a rate such as 50 or 100 per second as if it were a number of seconds.
Asked as 'the AC mains changes direction every ___' or 'how many times per second does 50 Hz AC reverse?'
No directly related past PYQ was found.
- practice — not a real PYQ
The frequency of the AC mains supply in India is 50 Hz. How many times does the current reverse its direction in one second?
- (a)25
- (b)50
- (c)100
- (d)200
Answer(c) 100 — the current reverses twice per cycle, and there are 50 cycles per second, so 2 x 50 = 100.
- practice — not a real PYQ
The time period of the AC supply used in Indian homes is:
- (a)1/50 s
- (b)1/100 s
- (c)50 s
- (d)100 s
Answer(a) 1/50 s — the time period equals 1/frequency = 1/50 s for a 50 Hz supply.