Study the circuits (a) and (b) shown in figure and answer the following questions.

(a) Under which conditions would the rms currents in the two circuits be the same ? (b) Can the rms current in circuit (b) be larger than that in (a) ?

Explanation

Let in circuit (a) rms current =`I_a` and in circuit (b) rms current = `I_b`
Now `I_a=V_"rms"/R=V/R`
`I_b=V_"rms"/Z=V/sqrt(R^2+(X_L-X_C)^2)`
(a) `I_a=I_b`
`therefore V/R = V/sqrt(R^2+(X_L-X_C)^2)`
`therefore R=sqrt(R^2+(X_L-X_C)^2)`
If `X_L=X_C` both are same , there is resonce condition.
`therefore` When `X_L=X_C` in both the circuit `I_(rms)` with be same.
(b) As `Z ge R`
`I_a/I_b=sqrt(R^2+(X_L-X_C)^2)/R=Z/R`
`therefore I_a/I_b=Z/R` but `Z ge R rArr Z/R ge 1`
`therefore I_a/I_b ge 1`
`therefore I_a ge I_b`
No, the rms current in circuit (b) cannot be larger than that in (a).