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Question
Choose the correct option.
If the rms current in a 50 Hz AC circuit is 5A, the value of the current 1/300 seconds after its value becomes zero is ______.
Options
`5sqrt2 A`
`5sqrt(3/2) A`
`5/6 A`
`5/sqrt2 A`
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Solution
If the rms current in a 50 Hz AC circuit is 5A, the value of the current 1/300 seconds after its value becomes zero is `5sqrt(3/2) A`.
Explanation:
Substitute the given values from,
Frequency = `f - 50 Hz` .....(1)
Current = `I = 5A` ......(2)
Time = `1/300 S` .....(3)
Let `I_O` be the peak value
Therefore, `I_O = sqrt(2)I` .....(4)
Put the values in equation (2) and (4) and calculate:
`I_O = sqrt(2) xx 5`
`I_O = 5sqrt(2)A` ......(5)
∵ `I = I_0 sin(wt)`` ......(6)
Put the values in equations (3), (5) and (6) and calculate:
Also, `I = 5sqrt(2) xx sin(2pi f xx 1/300)`
`I = 5sqrt(2) xx sin(100pi xx 1/300)`
`I = 5sqrt(2) xx sin 60`
`I = 5sqrt(2) xx sqrt(3)/2`
`I = 5 xx sqrt(3)/sqrt(2) A`
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