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Question
If the rms current in a 50 Hz ac circuit is 5 A, the value of the current 1/300 seconds after its value becomes zero is ______.
Options
`5sqrt(2)` A
`5sqrt(3/2)` A
`5/6` A
`5/sqrt(2)` A
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Solution
If the rms current in a 50 Hz ac circuit is 5 A, the value of the current 1/300 seconds after its value becomes zero is `underline(5sqrt(3/2) A)`.
Explanation:
Equation for i and V: Alternating current or voltage varying as sine function can be written as
`i = i_0 sin ωt = i_0 sin 2piv t = i_0 sin (2pi)/T t`
And `V = V_0 sin ωt = V_0 sin 2pivt = V_0 sin (2pi)/T t`
Where I and V are instantaneous values of current and voltage,
i0 and V0 are peak values of current and voltage
ω = Angular frequency on rad/sec, v = Frequency in Hz
T = TIme peroid
`I_(ωt) = I = sqrt(2)I_0 = 5sqrt(2)A`
`I = I_0 sin ωt`
At `t = 1/300 sec, I = 5sqrt(2) sin 2 pivt = 5sqrt(2) sin 2pi xx 50 xx 1/300`
= `5sqrt(2) sin pi/3 = 5sqrt(2) sin 60^circ`
= `52 - sqrt(3)sqrt(2)` = 532
= `5sqrt(3/2) A`
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