# Handout 1: Nodal Analysis

## Nodal analysis

- Count the number of nodes (\(N\)).
- Designate a reference node.
- Label the nodal voltages (\(N-1\) of them).
- Write a KCL equation for each of the nonreference nodes.
- Express any additional unknowns such as currents or voltages other than nodal voltages in terms of appropriate nodal voltages.
- Organize the equations.
- Solve the system of equations for the nodal voltages (\(N-1\) of them).

## Supernode analysis

- Count the number of nodes (\(N\)).
- Designate a reference node.
- Label the nodal voltages (\(N-1\) of them).
- If the circuit contains voltage sources, form a supernode about each one.
- Write a KCL equation for each nonreference node and for each supernode that does not contain the reference node.
- Relate the voltage across each voltage source to nodal voltages.
- Express any additional unknowns (i.e., currents or voltages other than nodal voltages) in terms of appropriate nodal voltages.
- Organize the equations.
- Solve the system of equations for the nodal voltages (\(N-1\) of them).

## Thinking Aloud Pair Problem Solving (TAPPS)

Students are paired and given a series of problems. The two students are given specific roles that switch with each problem: Problem Solver and Listener. The problem solver reads the problem aloud and talks through the solution to the problem. The listener follows all of the problem solver’s steps and catches any errors that occur. For the listener to be effective, he or she must also understand the reasoning process behind the steps. This may require the listener to ask questions if the problem solver’s thought process becomes unclear. The questions asked, however, should not guide the problem solver to a solution nor should they explicitly highlight a specific error except to comment that an error has been made.