Question

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

(a)

(b)

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

Answer 1

(I_rms) in (a) = `V_(rms)/R`

(I_rms) in b = `V_(rms)/Z = V_(rms)/sqrt(R^2 + (X_L - X_C))`

(a) (I_rms)a = (I_rms)b

∴ R =  `sqrt(R^2 + (X_L - X_C)^2)`

Squaring both sides

R² = R² + (X_L – X_C)²

Or  (X_L – X_C)² = 0

X_L = X_C

(b) For (I_rms)b > (I_rms)a

`V_(rms)/sqrt(R^2 + (X_L - X_C)^2) > V_(rms)/R`

As V_rms = V so,

`sqrt(R^2 + (X_L - X_C)^2) < R`

Squaring both sides

R² + (X_L – X_C)² < R²

(X_L – X_C)² < 0

Square of any number can never be negative. Reactance of X_L​ and X_C​ cannot be negative.

So the rms current in circuit (b) cannot be larger than that in (a).