Impara Kirchhoff's Laws in Python | Circuit Analysis with Python

Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL) are two foundational principles in circuit analysis that allow you to solve for unknown voltages and currents in complex circuits. KVL states that the algebraic sum of all voltages around any closed loop in a circuit is zero, ensuring energy conservation in electrical circuits. KCL states that the sum of currents entering a node (or junction) is equal to the sum of currents leaving the node, reflecting the conservation of electric charge. By applying these laws, you can analyze multi-loop circuits and solve for unknown quantities using systematic methods.


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import numpy as np

# Coefficient matrix for a two-loop circuit
# Suppose the equations are:
# 10*I1 + 2*I2 = 12
# 2*I1 + 8*I2 = 10

A = np.array([[10, 2],
              [2, 8]])

b = np.array([12, 10])

# Solve for currents I1 and I2
currents = np.linalg.solve(A, b)

print("I1 = {:.2f} A, I2 = {:.2f} A".format(currents[0], currents[1]))

To derive the equations used above, you start by labeling the currents in each loop of the circuit and assigning directions. For each loop, you apply Kirchhoff's Voltage Law (KVL) by summing the voltage drops (products of resistance and current) and setting their sum equal to the total voltage sources in that loop. If loops share components, the shared resistor's voltage drop is expressed in terms of both loop currents. This process results in a system of linear equations where the unknowns are the loop currents. Python, with the help of numpy, allows you to efficiently represent these equations as matrices and solve them rapidly, even for larger systems.


              1234567891011121314
            
import numpy as np

# Using the same system as before:
# 10*I1 + 2*I2 = 12
# 2*I1 + 8*I2 = 10

A = np.array([[10, 2],
              [2, 8]])
b = np.array([12, 10])

currents = np.linalg.solve(A, b)

print("The current in loop 1 (I1) is {:.2f} A".format(currents[0]))
print("The current in loop 2 (I2) is {:.2f} A".format(currents[1]))

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Sezione 1. Capitolo 6

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Suggested prompts:

Can you explain how to set up the equations for a different circuit?

What if the circuit has more than two loops?

Can you show how to apply KCL in a similar example?

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              12345678910111213141516
            
import numpy as np

# Coefficient matrix for a two-loop circuit
# Suppose the equations are:
# 10*I1 + 2*I2 = 12
# 2*I1 + 8*I2 = 10

A = np.array([[10, 2],
              [2, 8]])

b = np.array([12, 10])

# Solve for currents I1 and I2
currents = np.linalg.solve(A, b)

print("I1 = {:.2f} A, I2 = {:.2f} A".format(currents[0], currents[1]))


              1234567891011121314
            
import numpy as np

# Using the same system as before:
# 10*I1 + 2*I2 = 12
# 2*I1 + 8*I2 = 10

A = np.array([[10, 2],
              [2, 8]])
b = np.array([12, 10])

currents = np.linalg.solve(A, b)

print("The current in loop 1 (I1) is {:.2f} A".format(currents[0]))
print("The current in loop 2 (I2) is {:.2f} A".format(currents[1]))

Tutto è chiaro?

Grazie per i tuoi commenti!

Sezione 1. Capitolo 6

Kirchhoff's Laws in Python

1. What does Kirchhoff's Voltage Law state?

2. How can systems of equations be used to solve for unknowns in a circuit?

3. Why is Python useful for solving circuit equations?

Kirchhoff's Laws in Python

1. What does Kirchhoff's Voltage Law state?

2. How can systems of equations be used to solve for unknowns in a circuit?

3. Why is Python useful for solving circuit equations?