Practice Problems (KEY)

Practice Problems (KEY)#

Problem 1

  • Nodes: 4   Nodes: 6

  • Loops: 3   Loops: 7

  • Nodes: 4   Nodes: 4

  • Loops: 1   Loops: 7

Problem 2

\[V_1 = (2\,\text{mA})(1.5\,\text{k}\Omega) = 3\,\text{V}\]
\[V_S - V_1 - V_R = 0\]
\[V_R = V_S - V_1 = 9\,\text{V} - 3\,\text{V} = \boxed{6\,\text{V}}\]
\[V_R - V_P - V_{\text{out}} = 0\]
\[V_P = V_R - V_{\text{out}} = 6\,\text{V} - 2\,\text{V} = \boxed{4\,\text{V}}\]
Problem 3

Given \(i_2 = -2\,\text{A}\), \(i_3 = -5\,\text{A}\), and \(i_4 = 4\,\text{A}\):

\[i_5 + i_4 - i_3 = 0 \implies i_5 = -i_4 + i_3 = -(4\,\text{A}) + (-5\,\text{A}) = \boxed{-9\,\text{A}}\]
\[i_1 + i_2 + i_3 - i_4 = 0 \implies i_1 = -i_2 - i_3 + i_4 = -(-2) - (-5) + 4 = \boxed{11\,\text{A}}\]
Problem 4

(a) Nodes: 3   Loops: 3

(b) KVL and KCL equations:

  • \(V_Q - V_P - V_R = 0\)

  • \(V_R - V_S = 0\)

  • \(V_Q - V_P - V_S = 0\)

  • \(I_Q + I_P = 0\)

  • \(-I_P - I_R - I_S = 0\)

  • \(-I_Q + I_R + I_S = 0\)

(c) Power consumed by each component:

  • \(V_S = 4\,\text{V}\), \(V_R = 4\,\text{V}\), \(V_P = 6\,\text{V}\), \(V_Q = 10\,\text{V}\)

  • \(I_S = 1\,\text{A}\), \(I_R = 1\,\text{A}\), \(I_P = -2\,\text{A}\), \(I_Q = 2\,\text{A}\)

  • \(P_S = 4\,\text{W}\), \(P_R = 4\,\text{W}\), \(P_P = 12\,\text{W}\), \(P_Q = 20\,\text{W}\)

Problem 5

KVL Equations

KCL Equations

\(-V_G - 2\,\text{V} + V_J = 0\)

\(4\,\text{A} + I_H - 3\,\text{A} = 0\)

\(2\,\text{V} - 7\,\text{V} - V_K = 0\)

\(3\,\text{A} + I_J - 5\,\text{A} - 6\,\text{A} = 0\)

\(-V_L + V_K + 17\,\text{V} = 0\)

\(I_M + I_N + 5\,\text{A} = 0\)

\(-V_J + V_L - 6\,\text{V} = 0\)

\(6\,\text{A} - I_N - I_H = 0\)

\(V_G = 4\,\text{V}\)

\(I_M = -I_N - 5\,\text{A}\)
Problem 6

A satellite control module is connected to a data processing element modeled as a single \(12.5\,\text{k}\Omega\) resistor (\(R_2\)). The system is powered by a \(5\,\text{V}\) solar cell (\(V_S\)). Control module options:

  • \(R_1 = 5\,\text{k}\Omega\)

  • \(R_1 = 10\,\text{k}\Omega\)

  • \(R_1 = 15\,\text{k}\Omega\)

(Solved in class — see lecture notes for full solution.)

Problem 7

Requirements:

  • Total current must not exceed \(250\,\mu\text{A}\)

  • Voltage across the control module (\(V_1\)) must be at least \(2\,\text{V}\)

(Solved in class — see lecture notes for full solution.)