MHT CET · Physics · Alternating Current
An alternating current is given by \(I=100 \sin (50 \pi t)\). How many times will the current become zero in one second?
- A 50 times
- B 25 times
- C 40 times
- D 100 times
Answer & Solution
Correct Answer
(A) 50 times
Step-by-step Solution
Detailed explanation
Current is given by, \(\mathrm{I}=\mathrm{I}_0 \sin \omega t\)...(i)
Given, \(I=100 \sin (50 \pi t)\)
Comparing with (i),
\(\omega=50 \pi\)
\(\therefore \quad 2 \pi \mathrm{f}=50 \pi\)
\(\therefore \quad \mathrm{f}=25 \mathrm{~Hz} \Rightarrow 25\) cycles per second Current becomes zero twice in one cycle
\(\therefore \quad\) Current becomes zero, \(25 \times 2=50\) times
Given, \(I=100 \sin (50 \pi t)\)
Comparing with (i),
\(\omega=50 \pi\)
\(\therefore \quad 2 \pi \mathrm{f}=50 \pi\)
\(\therefore \quad \mathrm{f}=25 \mathrm{~Hz} \Rightarrow 25\) cycles per second Current becomes zero twice in one cycle
\(\therefore \quad\) Current becomes zero, \(25 \times 2=50\) times
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