Tag: electrical engineering basics

  • Solving a Circuit Using KVL and KCL 

    Solving a Circuit Using KVL and KCL 

    Use Kirchhoff’s Voltage Law (KVL) and Kirchhoff’s Current Law (KCL) to find V_x​ and I_y.

    Solving a Circuit Using KVL and KCL 

    Applying Kirchhoff’s Voltage Law (KVL)

    KVL states: The sum of all voltages in a closed loop is zero.

    Loop 1: 20V Source, 2Ω Resistor, and 5A Current Source

    We start with Loop 1 which is shown below.

    Solve Using KVl and KCL - Loop 1

    The KVL equation is:

        \[-20V - (2\Omega \cdot 2A) + V_{5A} = 0\]

    Simplify:

        \[-20V - 4V + V_{5A} = 0\]

        \[V_{5A} = 16V\]

    Loop 2: Voltage AcrossV_{5A}, 3V Source, and 7Ω Resistor

    Next, we analyze Loop 2 shown below:

    Solve Using KVl and KCL - Loop 2

    The equation is:

        \[-16V + 4V - (6\Omega \cdot I_y) = 0\]

    Simplify:

        \[-12V -6\Omega \cdot I_y = 0\]

        \[I_y = -2A\]

    KCL: Applying Kirchhoff’s Current Law (KCL)

    KCL states: The total current entering a node equals the total current leaving the node.

    At the middle node, the currents are:

        \[2A + 5A +(-2A) - I_{3\Omega} = 0\]

    Simplify:

        \[I_{3\Omega} = 5A\]

    Finding V_x

    Finally, we calculate V_x using KVL in Loop 3:

    Solve Using KVl and KCL - Loop 3

    The equation is:

        \[-16V + (3\Omega \cdot 5A) - V_x = 0\]

    Simplify:

        \[-16V + 15V - V_x = 0\]

        \[V_x = -1V\]

    Using Python to Solve the Circuit

    One powerful way to solve electrical circuits is by using the Lcapy library in Python. Lcapy is an open-source Python package designed for symbolic linear circuit analysis and signal processing.

    Below is an example of how to use Lcapy to solve the given circuit and find I_y (the current through V_2) and I_{R_1} (the current through the 2Ω resistor).

    Python Code to Solve the Circuit

    ```python
    from lcapy import Circuit
    cct = Circuit("""
    V1 1 0 20; down,
    R1 1 N_A 2; right=1.5, i=I_{R_1},
    I1 N_A 0_2 5; down, 
    W N_A 5; up=0.7, 
    R2 N_A 3 3; right=1.5, 
    V_x 0_3 3 -1; up, 
    V2 5 4 4; right=2, i=I_y,
    R4 0_4 4 6; up,
    W 0 0_2; right, 
    W 0_2 0_3; right, 
    W 0_3 0_4; right, 
    """)
    print(f"Current through R1 (I_R1): {cct.R1.i}")
    print(f"Current through V2 (I_y): {cct.V2.i}")

    which prints

    Current through R1 (I_R1): 2
    Current through V2 (I_y): -2