For a series LCR circuit the square of impedance is

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

For a series LCR circuit the square of impedance is Z2=R2+(ωL−1ωC)2Z^2 = R^2 + \left(\omega L - \dfrac{1}{\omega C}\right)^2. Which of the following is the correct expression for d(Z2)dω\dfrac{d(Z^2)}{d\omega}? (a) 2R2+(ωL−1ωC)2(L+1ω2C)2\sqrt{R^{2}+\left(\omega L-\dfrac{1}{\omega C}\right)^{2}}\left(L+\dfrac{1}{\omega^{2}C}\right) (b) 2(ωL−1ωC)L2\left(\omega L-\dfrac{1}{\omega C}\right)L (c) 2(ωL−1ωC)(L+1ω2C)2\left(\omega L-\dfrac{1}{\omega C}\right)\left(L+\dfrac{1}{\omega^{2}C}\right) (d) 2(ωL−1ωC)(L−1ω2C)2\left(\omega L-\dfrac{1}{\omega C}\right)\left(L-\dfrac{1}{\omega^{2}C}\right)

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