Solving a Circuit Using KVL and KCL 

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

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.

The KVL equation is:

   

Simplify:

   

   

Loop 2: Voltage Across, 3V Source, and 7Ω Resistor

Next, we analyze Loop 2 shown below:

The equation is:

   

Simplify:

   

   

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:

   

Simplify:

   

Finding

Finally, we calculate using KVL in Loop 3:

The equation is:

   

Simplify:

   

   

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 (the current through ) and (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