Example 2

Nerd Cafe

Let's determine the voltage at node A using nodal analysis step by step.

Step 1: Identify the Nodes

• Node A: The voltage at this node is 𝑉_𝐴, which we need to determine.

• Ground Node: The bottom of 𝑅₂ is connected to the ground (0V).

Step 2: Apply Kirchhoff’s Current Law (KCL) at Node A

Using KCL, the sum of all currents leaving node A must be zero:

$$\frac{V_{A}-12}{5k\Omega}+\frac{V_{A}}{2k\Omega}-1mA=0$$

Rewriting the equation:

$$\frac{V_{A}-12}{5000}+\frac{V_{A}}{2000}-0.001=0$$

By simplification, we have:

$$V_{A}\cong 4.86 \; V$$

Python script

Here’s a Python script that calculates 𝑉_𝐴 ​based on user input for V _1​. The script uses SymPy for solving the nodal equation.

def calculate_va():
    # Get V1 from the user
    V1 = float(input("Enter the value of V1 (in Volts): "))

    # Given circuit values
    R1 = 5000  # 5kΩ
    R2 = 2000  # 2kΩ
    I1 = 0.001  # 1mA

    # Calculate Va
    Va = ((V1 / R1) + I1) / ((1 / R1) + (1 / R2))

    print(f"Va (Voltage at node A) = {Va:.2f} V")

# Run the function
calculate_va()

Output

Va (Voltage at node A) = 4.86 V

Keywords

nodal analysis, kirchhoff's current law, KCL, circuit analysis, node voltage method, electrical engineering, electronic circuits, DC circuits, AC circuits, linear circuits, circuit solving techniques, voltage nodes, current sources, resistive circuits, mesh analysis, supernode, circuit theory, circuit equations, Ohm's law, engineering education, nerd cafe