By what percentage the impedance in an AC series circuit should be increased so that the power factor changes from `(1/2) "to" (1/4)` (when R is constant)?

Options

A. 0.2
B. 0.5
C. 0.25
D. 1

Answer

D

Explanation

Power factor, `cosphi=(R)/(Z)`
If R is constant, then `cos phi prop(1)/(Z)`
`therefore (Z_(1))/(Z_(2))=(cosphi_(1))/(cosphi_(2))=(1//4)/(1//2)=(1)/(2)`
`implies Z_(2)=2Z_(1)`
`therefore`Percentage change `=(2Z_(1)-Z_(1))/(Z_(1))xx100=100%`