Laplace transforms: Simple Electrical Network

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Problem Statement

Using the formulas



Solve the system when V0 = 50 V, L = 0.5 h, R = 60 Ω, C = 10-4 f, and the currents are initially zero.

Solution

Solve the system when V0 = 50 V, L = 0.5 h, R = 60 Ω, C = 10^{-4} f, and the currents are initially zero. Substituting numbers into the equations, we have

Applying the Laplace transform to each equation gives

Solving for gives