Question

1. (10 Points) Use node-voltage analysis to solve the circuit below and determine Ip. 80 kΩ 20 kΩ Ip 101P 100 k2 400 μΑ 40 VC-

Answer 1

I_p = v_2/100 k Ohm Apply Nodal analysis at v_1 v_1 - 40/8 k Ohm + 10 I_p + v_1 - v_2/20 k Ohm = 0 v_1 - 40/80 k Ohm + 10 v_2/100 k Ohm + v_1 - v_2/20 k Ohm = 0 \r\n 5v_1 - 200 + 40 v_2 + 20 v_1 - 20 v_2/400 k Ohm = 0 25 v_1 + 20 v_2 = 200 rightarrow (1) Apply Nodal Analysis at v_2 Therefore v_2 - v_1/20 k Ohm + v_2/100 k Ohm - 4/10 k = 0 5(v_2 - v_1) + v_2/100 k Ohm = 0.4 mA Rightarrow 6v_2 - 5v_1 = 40 rightarrow (2) (2) times 5 Rightarrow - 25 v_1 + 30 v_2 = 200 rightarrow (2) (1) + (2) Rightarrow 50 v_2 = 400 Therefore v_2 = 8v Therefore form (1) v_1 = 200 - 20 v_2/25 = 200 - 160/2 = 40/25 Therefore v_1 = 16v I_p = v_z/100 k Ohm = 8/100 k Ohm = 0.08 mA = 80 mu A Therefore I_p = 80 mu A