(Solved): Problem [1] Determine the equivalent capacitance. Problem [2] In the given circuit \( \mathrm{i}_{5 ...

Problem [1] Determine the equivalent capacitance. Problem [2] In the given circuit \( \mathrm{i}_{5}(t)=10 e^{-4 t} m A \). The initial values on the capacitors are \( \mathrm{v}_{1}(0)=20 \mathrm{~V} \) and \( \mathrm{v}_{2}(0)=30 \mathrm{~V} \). a) Determine \( v_{1}(t) \) b) Determine \( v_{2}(t) \) c) Determine the current on the 20 microfarad capacitor. Problem [3] The voltage across a \( 5-\mathrm{H} \) inductor is \( 10 e^{-3 t}+20 e^{-4 /} \mathrm{V} \). If the initial current through the inductor is \( 3 \mathrm{~A} \), find the current and the energy stored in the inductor at \( \mathrm{t}=2 \mathrm{~s} \).