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Question
An ideal inductor is connected across an AC source of voltage. The current in the circuit ______.
Options
is ahead of the voltage in phase by π.
lags voltage in phase by π.
is ahead of voltage in phase by `pi"/"2`.
lags voltage in phase by `pi"/"2`.
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Solution
An ideal inductor is connected across an AC source of voltage. The current in the circuit `underlinebb("lags voltage in phase by "pi"/"2)`.
Explanation:
`epsi = (-LdI)/(dt)`
`epsi_0 sinomegat = (-LdI)/(dt)`
In magnitude `(dI)/(dt) = epsi_0/L sinomegat`
On integrating both sides,
I = `intepsi_0/L sinomegat dt`
I = `epsi_0/L ((-1)/omega cosomegat)`
I = `-epsi_0/(Lomega) (cos omegat)`
I = `-epsi_0/(Lomega) sin(pi/2 - omegat)`
= `epsi_0/(Lomega) sin(omegat - pi/2)`
I = `I_0 sin(omegat - pi/2)`
Hence, current lags voltage in phase π/2.
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