If in a circuit lags behind EMF by `pi//2` . Then it is a/an

Options

A. resistor circuit
B. capacitor
C. inductor circuit
D. CR circuit

Answer

C

Explanation

Figure shows a purely inductive circuit, in which a sinusoidal emf is applied. The induced emf across the inductor is `-L(dt)/(dt)` so that from Kirchheffi's law,
`epsi_(0)sinomegat-L(dt)/(dt)=0`
`implies (dt)/(dt)=(epsi_(0))/(L)cosomegat+C`
The constant C can be shown to be zero from the fact , the emf being sinusoidal , the current should also be so, and the average current over one time period has to be zero.
`therefore i=-(epsi_(0))/(omegaL) cos omegat " or " i=(epsi_(0))/(omegaL) sin (omegat-pi//2)`
which shows that the current lags behind the emf by a phase of `pi//2`