Question

2. Consider the circuit shown below. sa 3 32 4A 8V 752 a. b. c. d. Write the nodal equations. Solve for the node voltages Calculate the loop currents. What is the voltage across the 2Ω resistor.

Answer 1

Here, we found current and voltages by using KCL and KCL and applied nodal equations for that as -

We have a) Here we get three nodal equations as: - At node 1 p - v/3 + f - v_1/5 = > 0 At node 2: - 4 = > v - 8/3 + v/2 At node 3 v_1/13 Ohm + v_1- 8/5 = > 4 = > 0 \r\n at node 1 p -v/3 + f -v_1/5 = > 0 8/3 + 8/5 = > v/3 + v_1/5 = > v/3 + v_1/5 = > 64/15 - (1) at node 2 4 = > v/2 + v - 8/3 4 = > v/2 + v/3 - 8/3 = > 5 v/6 = > 4 + 8/3 = > 20/3 v = > 20 times 6/3 times 5 = > 8 v \r\n at node 3 V_1/13 + v_1 - 8/5 + 4 = > 0 v_1/13 + v_1/5 = > 4 - 1,0 v_1 = > -8.666 v c)Noe for loop currents \r\n for I_2, we know v_1 i_2 = > -v_1/3 = > 0.666 A at node 3 we get i_3 = > 4 + i_2 i_3 =.3,33 A for applying K c L at node 2 we get