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Question
Study the circuits (a) and (b) shown in figure and answer the following questions.
 (a) |
 (b) |
- 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)?
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Solution
(Irms) in (a) = `V_(rms)/R`
(Irms) in b = `V_(rms)/Z = V_(rms)/sqrt(R^2 + (X_L - X_C))`
(a) (Irms)a = (Irms)b
∴ R = `sqrt(R^2 + (X_L - X_C)^2)`
Squaring both sides
R2 = R2 + (XL – XC)2
Or (XL – XC)2 = 0
XL = XC
(b) For (Irms)b > (Irms)a
`V_(rms)/sqrt(R^2 + (X_L - X_C)^2) > V_(rms)/R`
As Vrms = V so,
`sqrt(R^2 + (X_L - X_C)^2) < R`
Squaring both sides
R2 + (XL – XC)2 < R2
(XL – XC)2 < 0
Square of any number can never be negative. Reactance of XL and XC cannot be negative.
So the rms current in circuit (b) cannot be larger than that in (a).
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