In an LCR series circuit, source of emf is : E = 30sin(100t) and R =…

The correct answer is Option (4) → (D), (C), (B), (A)

Read the angular frequency from the emf and find each reactance, then the impedance of the series circuit.

    \( \omega = 100\,\mathrm{rad/s} \)
    \( L = 100\,\mathrm{mH} = 0.1\,\mathrm{H} \)
    \( C = 100\,\mu\mathrm{F} = 10^{-4}\,\mathrm{F} \)

    (D) The numerical value of inductive reactance — \( X_L = \omega L = 100 \times 0.1 = 10\,\Omega \)

    (C) The numerical value of capacitive reactance — \( \displaystyle X_C = \frac{1}{\omega C} = \frac{1}{100 \times 10^{-4}} = 100\,\Omega \)

    (B) The numerical value of Resistance R — \( R = 120\,\Omega \)

    (A) The numerical value of impedance — \( \displaystyle Z = \sqrt{R^{2} + (X_C - X_L)^{2}} = \sqrt{120^{2} + 90^{2}} = \sqrt{22500} = 150\,\Omega \)

    \( 10 \lt 100 \lt 120 \lt 150 \)

The increasing order is (D), (C), (B), (A).