Question

An ideal inductor is connected across an AC source of voltage. The current in the circuit ______.

विकल्प

• 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`.

Answer 1

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.