LC Circuits Video Lessons

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# Problem: Consider an L-C circuit with capacitance C, inductance L, and no voltage source, as shown in the figure (Figure 1). As a function of time, the charge on the capacitor is Q(t) and the current through the inductor is I(t). Assume that the circuit has no resistance and that at one time the capacitor was charged.Part A. As a function of time, what is the energy UL(t) stored in the inductor? Express your answer in terms of L and I(t).UL(t) = Part B. As a function of time, what is the energy UC(t) stored in the inductor? Express your answer in terms of C and Q(t).UC(t) =

###### FREE Expert Solution

Energy stored in a magnetic field:

$\overline{){\mathbf{U}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{L}}{{\mathbf{i}}}^{{\mathbf{2}}}}$

Energy stored in a capacitor:

$\overline{){\mathbf{U}}{\mathbf{=}}\frac{\mathbf{Q}\mathbf{V}}{\mathbf{2}}{\mathbf{=}}\frac{\mathbf{C}{\mathbf{V}}^{\mathbf{2}}}{\mathbf{2}}{\mathbf{=}}\frac{{\mathbf{Q}}^{\mathbf{2}}}{\mathbf{2}\mathbf{C}}}$

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###### Problem Details

Consider an L-C circuit with capacitance C, inductance L, and no voltage source, as shown in the figure (Figure 1). As a function of time, the charge on the capacitor is Q(t) and the current through the inductor is I(t). Assume that the circuit has no resistance and that at one time the capacitor was charged.

Part A. As a function of time, what is the energy UL(t) stored in the inductor?

UL(t) =

Part B. As a function of time, what is the energy UC(t) stored in the inductor? Express your answer in terms of C and Q(t).

UC(t) =