All Problems Electric Oscillations
Problem 4.145
A capacitor with capacitance \(C=1.0 \mu \mathrm{F}\) and a coil with active resistance \(R=0.10 \Omega\) and inductance \(L=1.0 \mathrm{mH}\) are connected in parallel to a source of sinusoidal voltage \(V=31 \mathrm{~V}\). Find: (a) the frequency \(\omega\) at which the resonance sets in; (b) the effective value of the fed current in resonance, as well as the corresponding currents flowing through the coil and through the capacitor.
4.145. (a) \(\omega_{r e s}=\sqrt{\frac{1}{L C}-\frac{R^{2}}{L^{2}}}=3 \cdot 10^{4} \mathrm{rad} / \mathrm{s}\) (b) \(I=V R C / L=\) \(=3 \mathrm{~mA}, \quad I_{L}=V \sqrt{C / L}=1.0 \mathrm{~A}, \quad I_{C}=V \sqrt{\frac{C}{L}-\left(\frac{R C}{L}\right)^{2}}=1.0 \mathrm{~A} .\)