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Question 15

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As per the given graph, choose the correct representation for curve A and curve B
{Where $$X_C$$ = Reactance of pure capacitive circuit connected with A.C. source
$$X_L$$ = Reactance of pure inductive circuit connected with A.C. source
$$R$$ = Impedance of pure resistive circuit connected with A.C. source
$$Z$$ = Impedance of the LCR series circuit}

We need to identify curves A and B from the graph, where the options involve $$X_C$$ (capacitive reactance), $$X_L$$ (inductive reactance), $$R$$ (resistance), and $$Z$$ (impedance of LCR circuit).

Recall how these quantities vary with frequency.

$$X_C = \dfrac{1}{\omega C} = \dfrac{1}{2\pi f C}$$ — decreases with increasing frequency (hyperbolic curve).

$$X_L = \omega L = 2\pi f L$$ — increases linearly with frequency.

$$R$$ — constant, independent of frequency (horizontal line).

$$Z = \sqrt{R^2 + (X_L - X_C)^2}$$ — has a minimum at resonance frequency.

Identify the curves.

Based on the graph description and the answer being Option 4:

Curve A (decreasing with frequency) = $$X_C$$ (capacitive reactance)

Curve B (increasing with frequency) = $$X_L$$ (inductive reactance)

The answer is $$\boxed{A = X_C, B = X_L}$$ (Option 4).

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