After differentiating with respect to for a series LCR circuit

PHYSICS · Single correct · CBSE · Physics · Alternating Current · Alternating Current

Problem

After differentiating Z2Z^2 with respect to ω\omega for a series LCR circuit, two factors appear: (ωL−1ωC)\left(\omega L - \dfrac{1}{\omega C}\right) and (L+1ω2C)\left(L + \dfrac{1}{\omega^{2} C}\right). To obtain the finite angular frequency at which the impedance is minimum, which factor must be set equal to zero? (a) Only (L+1ω2C)=0\left(L+\dfrac{1}{\omega^{2}C}\right)=0 (b) Only (ωL−1ωC)=0\left(\omega L-\dfrac{1}{\omega C}\right)=0 (c) Both factors must simultaneously be zero (d) Neither; the impedance is minimum when ω=0\omega=0

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