Question 424: AC fundamentals

Question

In a series $L C R$ circuit $R=300 \Omega, L=0.9 \mathrm{H}$, $C=2 \mu \mathrm{~F}, \omega=1000 \mathrm{rad} / \mathrm{s}$. The impedance of the circuit is

Accepted Answer

Key Idea Impedance for series $\angle C R$ circuit is given by $Z=\sqrt{R^2+\left(\omega L-\frac{1}{\omega C}ight)^2}$
Given, resistance, $R=300 \Omega$, inductance, $L=0.9 \mathrm{H}$, capacitance, $C=2 \mu \mathrm{~F}=2 	imes 10^{-6} \mathrm{~F}$ and angular frequency, $\omega=1000 \mathrm{~rad} / \mathrm{s}$.
Substituting the given values in the above equation, we get
$$\begin{array}{ll}
\Rightarrow & Z=\sqrt{300^2+\left(1000 	imes 0.9-\frac{1}{1000 	imes 2 	imes 10^{-6}}ight)^2} \
\Rightarrow & Z=\sqrt{90000+(900-500)^2} \
\Rightarrow & Z=\sqrt{250000}=500 \Omega
\end{array}$$
Hence, the impedance of $L C R$ circuit is $500 \Omega$

Answer

$500 \Omega$

Answer

$1300 \Omega$

Answer

$400 \Omega$

Answer

$900 \Omega$

AC fundamentals

In a series L C R circuit R=300 \Omega, L=0.9 \mathrm{H}, C=2 \mu \mathrm{~F}, \omega=1000 \mathrm{rad} / \mathrm{s}. The impedance of the circuit is

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