All Problems

Electric Oscillations

Problem 4.109

In a circuit shown in Fig. 4.29 the battery emf is equal to E=2.0 V,\mathscr{E}=2.0 \mathrm{~V}, its inter-nal resistance is r=9.0Ωr=9.0 \Omega, the capacitance of the capacitor is C=10μF,C=10 \mu \mathrm{F}, the coil inductance is L=100mH,L=100 \mathrm{mH}, and the resistance is R=1.0ΩR=1.0 \Omega. At a certain moment the switch SwS w was disconnected. Find the energy of oscillations in the circuit (a) immediately after the switch was disconnected; (b) t=0.30t=0.30 s after the switch was disconnected.

Reveal Answer
4.109.(a)W0=1/2=W0etR/L=0.10 mJ\begin{aligned} & 4.109 .(\mathrm{a}) W_{0}=1 / 2 \\ =& W_{0} \mathrm{e}^{-t R / L}=0.10 \mathrm{~mJ} \end{aligned}