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Electric Oscillations

Problem 4.145

A capacitor with capacitance C=1.0μFC=1.0 \mu \mathrm{F} and a coil with active resistance R=0.10ΩR=0.10 \Omega and inductance L=1.0mHL=1.0 \mathrm{mH} are connected in parallel to a source of sinusoidal voltage V=31 VV=31 \mathrm{~V}. Find: (a) the frequency ω\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.

Reveal Answer
4.145. (a) ωres=1LC−R2L2=3⋅104rad/s\omega_{r e s}=\sqrt{\frac{1}{L C}-\frac{R^{2}}{L^{2}}}=3 \cdot 10^{4} \mathrm{rad} / \mathrm{s} (b) I=VRC/L=I=V R C / L= =3 mA,IL=VC/L=1.0 A,IC=VCL−(RCL)2=1.0 A.=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} .
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