The frequency of an alternating current is 3 Hz. It implies that
- (a)there are 6 cycles/s
- (b)there are 3 cycles/s
- (c)there are 2 cycles/s
- (d)there is only 1 cycle/s
Correct — B, there are 3 cycles/s. Frequency is defined as the number of complete cycles an alternating quantity makes in one second, and its unit — the hertz (Hz) — literally means 'cycles per second'. So a frequency of 3 Hz means the current completes exactly 3 full cycles every second.
- (a)there are 6 cycles/s — 6 cycles per second would be 6 Hz, double the stated value. This doubling usually comes from counting the two direction-reversals inside each cycle, but frequency counts complete cycles, not reversals.
- (c)there are 2 cycles/s — 2 cycles per second is 2 Hz, which does not match the given 3 Hz.
- (d)there is only 1 cycle/s — 1 cycle per second is 1 Hz; the question specifies 3 Hz, so three cycles occur each second.
Frequency (f) measures how many complete oscillations or cycles a periodic quantity — such as an alternating current — completes per unit time. Its SI unit is the hertz (Hz); one hertz equals one cycle per second. Frequency and time period T are reciprocals: f = 1/T.
The trap is to over-read 'implies'. Because 1 Hz is simply 1 cycle/s, 3 Hz is just 3 cycles/s. Doubling to 6 tempts students who recall that AC reverses direction twice per cycle, but that counts reversals, not cycles.
- One hertz (Hz) equals one complete cycle per second.
- Household AC in India has a frequency of 50 Hz, i.e. 50 cycles per second.
- Frequency and time period are reciprocals: f = 1/T, so 3 Hz corresponds to a period of 1/3 second.
- In each AC cycle the current reverses direction twice, so 3 Hz means 6 direction-reversals per second even though there are only 3 cycles.
A frequency of 3 hertz simply means three full cycles per second.
- Confusing direction-reversals per second with cycles per second.
- Mixing up frequency (in hertz) with the time period (in seconds).
Usually a one-line definition check — 'a frequency of n Hz means how many cycles per second?' — where the answer is simply n.
Assertion (A): In our houses, the current in AC electricity line changes direction 60 times per second. Reason (R): The frequency of alternating voltage supplied is 60 hertz.
- (a) Both A and R are individually true and R is the correct explanation of A
- (b) Both A and R are individually true but R is not the correct explanation of A
- (c) A is true but R is false
- (d) A is false but R is true
Answer(a) Both A and R are individually true and R is the correct explanation of A
Same concept — the frequency of an alternating supply is measured in hertz, i.e. cycles per second, exactly the definition used here to read 3 Hz as 3 cycles/s.
- practice — not a real PYQ
The time period of an alternating current of frequency 50 Hz is
- (a)0.02 s
- (b)0.5 s
- (c)50 s
- (d)5 s
Answer(a) 0.02 s — T = 1/f = 1/50 = 0.02 s.
- practice — not a real PYQ
In one complete cycle, an alternating current reverses its direction
- (a)once
- (b)twice
- (c)thrice
- (d)not at all
Answer(b) twice — the current goes positive then negative once each cycle.