The following series $L-C-R$ circuit, when driven by an emf source of angular frequency 70 kilo-radians per…
- purely resistive circuit
- series R-L circuit
- series R-C circuit
- series L-C circuit with R = 0
Solution
Impedance, $Z=\sqrt{\left(X_L \sim X_C\right)^2+R^2}$ or $\quad Z=\sqrt{\left(\omega L \sim \frac{1}{\omega C}\right)^2+R^2}$ Inductive reactance $\begin{aligned} X_L & =\omega L=70 \times 10^3 \times 100 \times 10^{-6} \\ & =7 \Omega \end{aligned}$ Capacitance reactance $\begin{aligned} X_C & =\frac{1}{\omega C}=\frac{1}{70 \times 10^3 \times 1 \times 10^{-6}} \\ & =\frac{1}{7 \times 10^{-2}}=\frac{10^2}{7}=\frac{100}{7} \end{aligned}$ As $\quad X_C>X_L$ Hence, circuit behave like as $R-C$ circuit.
Asked in: AP EAMCET 2009