What is the energy supplied by the dc voltage source

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Reference no: EM132370030

Problem 1 - Consider the dc circuit shown below where all of the elements are ideal. The switch is closed at t = 0. Prior to closing the switch, the capacitor voltage is zero, (i.e. v_C(0^-) = 0).

1. Derive and sketch v_C(t), i_C(t) and i_S(t) for t ≥ 0.

2. What is the energy supplied by the dc voltage source (E_S) and the energy stored in the capacitor (E_C) from the time the switch is closed to after the switch has been closed for a long time (i.e., from t = 0^- t → ∞)?

3. How do v_C(t), i_C(t), i_S(t), E_S and E_C change if the value of the resistance R is made smaller and smaller until R → 0?

Problem 2 - Consider the dc circuit shown below where all of the elements are ideal. Assume that capacitance values are identical (C₁ = C₂ = C). The switch is closed at t = 0. Prior to closing the switch, the capacitor C₁ is charged to V_s while C₂ is uncharged (i.e. v_C1(0^-) = V_s, v_C2(0^-) = 0).

1. Determine the capacitor voltage and current waveforms for t ≥ 0.

2. What is the energy stored in the capacitors at t = 0^-? What is the energy stored in the capacitors after the switch has been closed for a long time (as t → ∞)? Is there a difference between the stored energies at t = 0^- and t = ∞? Explain.

Problem 3 - Consider the dc-excited LC circuit shown below where all of the elements are ideal. The switch is closed at t = 0. Prior to closing the switch, the capacitor voltage and inductor current are both zero, (i.e. v_C(0^-) = 0, i_L(0^-) = 0).

1. Derive and sketch v_C(t) and i_L(t) for t ≥ 0.

2. What is the energy supplied by the dc voltage source (E_S), the energy stored in the capacitor (E_C), and the energy stored in the inductor (E_L) from the time the switch is closed to after the switch has been closed for a long time (i.e., from t = 0^- to t → ∞)? What is the relationship between E_S, E_C and E_L.

Reference no: EM132370030

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