Calculate the values of i2, i3, v2, v3, va, vc and vL of the network s

1.	Calculate the values of i2, i3, v2, v3, va, vc and vL of the network shown in Fig. 5.40 at the following times : (i) At time, t = 0 + immediately after the switch S is closed ; (ii) At time, t → ∞ i.e. in the steady state.
Answer» (i) In this case the coil acts as an open circuit, hence i₂ = 0 ; v₂ = 0 and v_L = 20 V. Since a capacitor acts as a short circuit i₃ = 20/(5 + 4) = 9 = 20/9 A. Hence, v₃ = (20/9) × 4 = 80/9 V and v_c = 0. (ii) Under steady state conditions, capacitor acts as an open circuit and coil as a short circuit. Hence, i₂ = 20/ (5 + 7) = 20/12 = 5/3 A; v₂ = 7 × 5/3 = 35/3 V; v_L = 0. Also i₃ = 0, v₃ = 0 but v_c = 20V.

Calculate the values of i2, i3, v2, v3, va, vc and vL of the network shown in Fig. 5.40 at the following times : (i) At time, t = 0 + immediately after the switch S is closed ; (ii) At time, t → ∞ i.e. in the steady state.

Answer»

(i) In this case the coil acts as an open circuit, hence i₂ = 0 ; v₂ = 0 and v_L = 20 V.

Since a capacitor acts as a short circuit i₃ = 20/(5 + 4) = 9 = 20/9 A. Hence, v₃ = (20/9) × 4 = 80/9 V and v_c = 0.

(ii) Under steady state conditions, capacitor acts as an open circuit and coil as a short circuit. Hence, i₂ = 20/ (5 + 7) = 20/12 = 5/3 A; v₂ = 7 × 5/3 = 35/3 V; v_L = 0.

Also i₃ = 0, v₃ = 0 but v_c = 20V.

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Calculate the values of i2, i3, v2, v3, va, vc and vL of the network shown in Fig. 5.40 at the following times : (i) At time, t = 0 + immediately after the switch S is closed ; (ii) At time, t → ∞ i.e. in the steady state.

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