Study the circuit (a) and (b) shown in Fig. and answer the following questions.
(a) Under which conditions would the rms currents in the two circuits be the same ?
Can the rms current in circuit (b) be larger than that in (a) ?

Answer

A

Explanation

Let, `(I_("rms"))a`=rms current in circuit (a)
`(I_("rms"))b`=rms current in circuit (b)
`(I_("rms"))a=V_(rms)/R =V/R`
`(I_("rms"))b=V_("rms")/Z=V/sqrt(R^(2)+(X_(L)-X_(C))^(2)`
a) When `(I_("rms"))a=(I_("rms"))b`
`R=sqrt(R^(2) + (X_(L)-X_(C))^(2)`
`rArr X_(L) = X_(C)`, resonance condition.
b) As `Z gt-R`
`rArr (I_("rms")a)/(I_("rms")b)=sqrt(R^(2)+(X_(L)-X_(C))^(2)/R`
`=Z/R `
`rArr (I_("rms"))agt-(I_("rms"))b`
No, the rms current in circuit (b), cannot be larger than that in a).