Practice Problems (KEY)

Practice Problems (KEY)#

How many nodes and how many loops are in each of the circuits below?

Nodes:4________ Nodes:6______

Loops:3_______ Loops:7_____

Nodes:4______ Nodes:4_____

Loops:1_______ Loops:7____

Find \(V_{R}\) and \(V_{P}\)

\[ V_{1} = (2\ \text{mA})(1.5\ \text{k}\Omega) = 3\ \text{V} \]
\[ V_{S} - V_{1} - V_{R} = 0 \]
\[ V_{R} = V_{S} - V_{1} = 9\ \text{V} - 3\ \text{V} = 6\ \text{V} \]
\[ V_{R} - V_{P} - V_{\text{out}} = 0 \]
\[ V_{P} = V_{R} - V_{\text{out}} = 6\ \text{V} - 2\ \text{V} = 4\ \text{V} \]

If \(i_{2} = -2\ \text{A}\), \(i_{3} = -5\ \text{A}\), and \(i_{4} = 4\ \text{A}\), then find \(i_{1}\) and \(i_{5}\).

\[ i_{5} + i_{4} - i_{3} = 0 \]
\[ i_{5} = -i_{4} + i_{3} = -(4\ \text{A}) + (-5\ \text{A}) = -9\ \text{A} \]
\[ i_{1} + i_{2} + i_{3} - i_{4} = 0 \]
\[ i_{1} = -i_{2} - i_{3} + i_{4} = -(-2\ \text{A}) - (-5\ \text{A}) + 4\ \text{A} = 11\ \text{A} \]

  1. Answer the following questions about the circuit below

a. How many nodes and loops are in this circuit?

Nodes: 3; Loops: 3

b. Write out the KVL and KCL equations for the circuit.

\(V_{Q} - V_{P} - V_{R} = 0\)
\(V_{R} - V_{S} = 0\)
\(V_{Q} - V_{P} - V_{S} = 0\)
\(I_{Q} + I_{P} = 0\)
\(-I_{P} - I_{R} - I_{S} = 0\)
\(-I_{Q} + I_{R} + I_{S} = 0\)

c. Solve for the power consumed by each component in this circuit

\(V_{S} = 4\ \text{V}\); \(V_{R} = 4\ \text{V}\); \(V_{P} = 6\ \text{V}\); \(V_{Q} = 10\ \text{V}\)
\(I_{S} = 1\ \text{A}\); \(I_{R} = 1\ \text{A}\); \(I_{P} = -2\ \text{A}\); \(I_{Q} = 2\ \text{A}\)
\(P_{S} = 4\ \text{W}\); \(P_{R} = 4\ \text{W}\); \(P_{P} = 12\ \text{W}\); \(P_{Q} = 20\ \text{W}\)

  1. Use KVL and KCL to solve for the unknown voltages and currents in the circuits below

\(-V_{G} - 2\ \text{V} + V_{J} = 0\)

\(4\ \text{A} + I_{H} - 3\ \text{A} = 0\)

\(2\ \text{V} - 7\ \text{V} - V_{K} = 0\)

\(3\ \text{A} + I_{J} - 5\ \text{A} - 6\ \text{A}\)

\(-V_{L} + V_{K} + 17\ \text{V} = 0\)

\(I_{M} + I_{N} + 5\ \text{A} = 0\)

\(-V_{J} + V_{L} - 6\ \text{V} = 0\)

\(6\ \text{A} - I_{N} - I_{H} = 0\)

\(V_{G} = 4\ \text{V}\)

\(I_{M} = -I_{N} - 5\ \text{A}\)

  1. A satellite control module is to be hooked to a data processing element, modeled as a single \(12.5\ \text{k}\Omega\) resistor (\(R_{2}\)). The entire system will be powered by a \(5\ \text{V}\) solar cell (\(V_{s}\)). Different options for the control module are modeled as \(R_{1} = 5\ \text{k}\Omega\), \(10\ \text{k}\Omega\), or \(15\ \text{k}\Omega\) resistors.

  2. If the circuit in the previous problem had the following two requirements, which of the three options are viable?

  • Total current cannot exceed \(250\ \mu\text{A}\)

  • Voltage across the control module (\(V_{1}\)) must be at least \(2\ \text{V}\)