Practice Problems

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

• Nodes: ____________ Nodes: ____________

• Loops: ____________ Loops: ____________

• Nodes: ____________ Nodes: ____________

• Loops: ____________ Loops: ____________

Find \(V_R\) and \(V_P\).

3. If \(i_2=-2\,\mathrm{A}\), \(i_3=-5\,\mathrm{A}\), and \(i_4=4\,\mathrm{A}\), find \(i_1\) and \(i_5\).

4. Answer the following questions about the circuit below.

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

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

c. Solve for the power consumed by each component in this circuit
(remember what we learned in the last lesson).

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

6. A satellite control module is to be connected to a data processing element modeled as a single \(12.5\,\mathrm{k}\Omega\) resistor (\(R_2\)). The entire system is powered by a \(5\,\mathrm{V}\) solar cell (\(V_S\)). Different options for the control module are modeled as \(R_1=5\,\mathrm{k}\Omega\), \(10\,\mathrm{k}\Omega\), or \(15\,\mathrm{k}\Omega\). For each option, calculate the values in the table below.

Option	Vs	R1	V1	V2	I1	I2	P1	P2	Ps
A	5 V	5 kΩ
B	5 V	10 kΩ
C	5 V	15 kΩ

7. If the circuit in the previous problem has the following requirements, which of the three options are viable?

Requirements:

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

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