GATE-2018 (24) :Wyllie – Time average equation

 

24) In a Electromagnetic measurement the resultant filed shows a phase lag of 30⁰ with respect to the primary field at the receiver coil. The ration of In phase to the Quadrature component of the resultant field is _____

 (Thanks to Chandrasekhar, ANU)

Solution:

Given that the Phase lag($\phi $) = 30⁰

 

 Then we know that the $\tan\phi=\frac{Quadrature component}{In phase}$

 

$\tan30=\frac{Quadrature component}{In phase}$

 

$\frac{1}{\sqrt{3}}=\frac{Quadrature component}{In phase}$

 

$\frac{In pahse}{Quadrature component}=\sqrt{3}$

 

$\frac{In pahse}{Quadrature component}=1.732$

 

The Ratio of In Phase to the Quadrature component of the resultant field is 1.732