AskSia

Plus

ca l node voltage equations

Aug 21, 2024

ca l node voltage equations

Answer

To find the node voltage equations for the given circuit, we will apply Kirchhoff's Current Law (KCL) at the nodes and express the voltages in terms of the known quantities.

Solution

Identify Nodes: Let's label the nodes in the circuit. Assume we have a reference node (ground) and label the other nodes as Node 1 and Node 2

Apply KCL at Node 1: According to KCL, the sum of currents entering a node equals the sum of currents leaving the node. For Node 1, we can express the currents through the resistors and the current sources in terms of the node voltages. If

V_1

is the voltage at Node 1, the currents can be expressed as:

I_{R1} = \frac{V_1 - V_{source}}{R_1}, \quad I_{R2} = \frac{V_1 - V_{2}}{R_2}, \quad I_{source1} = 1A, \quad I_{source2} = 2A

Thus, the KCL equation becomes:

I_{R1} + I_{source1} - I_{R2} - I_{source2} = 0

Substituting the expressions for the currents gives us the first equation

Apply KCL at Node 2: Similarly, for Node 2, we can express the currents in terms of the node voltages. If

V_2

is the voltage at Node 2, the KCL equation will be:

I_{R2} + I_{source2} - I_{R3} = 0

Where

I_{R3} = \frac{V_2 - V_{ground}}{R_3}

. Substituting gives us the second equation

Key Concept

Node Voltage Method

Explanation

The node voltage method involves applying KCL at the nodes of a circuit to derive equations that relate the node voltages to the currents and resistances in the circuit.