A solenoid with inductance `L=7 m H` and active resistance `R=44 Omega` is first connected to a source of direct voltabe `V_(0)` and then to a source of sinusoidal voltage with effective value `V=V_(0)` . At what frequency of the oscillator will be power consumed by the solenoid be `eta=5.0 ` times less than in the former case ?

Explanation

`P_(d.c.) =(V_(0)^(2))/(R)`
`P_(a.c.) =(V_(0)^(2))/( sqrt(R^(2)+omega^(2)L^(2))).(R)/( sqrt(R^(2)+omega^(2)L^(2)))=(v_(0)^(2)R)/( 1+ ((omegaL)/( R))^(2))=(P_(d.c.))/(eta)`
Thus `(omegaL)/( R) =sqrt(eta-1)`
or ` omega =(R)/( L) sqrt(eta-1)`
`v=(R)/( 2 pi L)sqrt(eta-1)=2 k H` of on putting the values.