MCQEasyJEE 2023Alternating Current Basics

JEE Physics 2023 Question with Solution

As per the given graph, choose the correct representation for curve AA and curve BB.

(Where XL=X_L = reactance of pure inductive circuit connected with A.C. source, XC=X_C = reactance of pure capacitive circuit connected with A.C. source, and R=R = impedance of pure resistive circuit connected with A.C. source, and Z=Z = impedance of the LCR series circuit)

  • A

    A=XL,B=RA = X_L, B = R

  • B

    A=XL,B=XCA = X_L, B = X_C

  • C

    A=XC,B=RA = X_C, B = R

  • D

    A=XC,B=XLA = X_C, B = X_L

Answer

Correct answer:D

Step-by-step solution

Standard Method

Given: The graph shows variation of impedance with frequency.

Find: Which physical quantities are represented by curve AA and curve BB.

For a pure inductor,

XL=ωLX_L = \omega L

so inductive reactance increases with frequency.

For a pure capacitor,

XC=1ωCX_C = \frac{1}{\omega C}

so capacitive reactance decreases with frequency.

Thus, the curve that decreases with frequency represents XCX_C, and the curve that increases with frequency represents XLX_L.

Therefore, A=XCA = X_C and B=XLB = X_L. The correct option is D.

Common mistakes

  • Confusing the frequency dependence of reactances. XLX_L increases with frequency, but XCX_C decreases with frequency. Use XL=ωLX_L = \omega L and XC=1ωCX_C = \frac{1}{\omega C} to decide correctly.

  • Treating resistance RR as frequency dependent in a pure resistive circuit. A pure resistor does not show this rising or falling behavior with frequency, so do not assign a varying curve to RR.

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