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KIRCHHOFF’S FIRST LAW
INTRODUCTION
Kirchhoff’s first law, generally known as the conservation of charge, asserts that « the algebraic sum of current at any junction in an electrical circuit is zero. »We may find any inconsistencies or deviations in circuit values by applying this formula at various junctions in a circuit.This rule is important to modern measuring techniques and is frequently applied in electrical engineering.
This rule determines how current is dispersed in a circuit, is vital in electrical circuit design, and is critical in recognizing defects or irregularities in electrical systems.This equation is a handy tool for solving a wide range of electrical circuit difficulties.In this topic, let us look into this law.
KIRCHHOFF’S FIRST LAW
This law is based on LAW OF CONSERVATION OF CHARGES.This law is widely used in electrical engineering.The current law relies on the fact that the net charge in the wires and components is constant.The current law is applicable to any lumped network irrespective of the nature of the network.
KIRCHHOFF’S FIRST LAW – STATEMENT
Kirchhoff’s first law states that « IN AN ELECTRIC CIRCUIT, THE ALGEBRAIC SUM OF CURRENT AT ANY JUNCTION IS ZERO ».
TOTAL CURRENT ENTERING A JUNCTION EQUALS TOTAL CURRENT LEAVING THE JUNCTION.
Current flowing towards the junction is taken as POSITIVE and current flowing away from the junction is taken as NEGATIVE.
KIRCHHOFF’S FIRST LAW-IMAGE
KIRCHHOFF’S FIRST LAW- EXAMPLE
Analogy to understand Kirchhoff’s First law
Imagine a water pipe system
- A pipe splits into multiple smaller pipes.
- The total amount of water entering the main pipe must equal to the total amount of water leaving through the smaller pipes.
Why is Kirchhoff’s first law important?
Solves complex circuits:
It helps analyze circuits with multiple branches and components.
Foundation for circuit analysis:
It is used alongside Kirchhoff’s second law (voltage law) to solve for unknown currents and voltages.
Real-life Applications:
It is used in designing electrical systems from small circuits to large power grids.
Numerical on Kirchhoff’s first law:
Question-1
In a circuit, four wires meet at a junction. The currents entering the junction are 15 A, 5 A and 3 A and the currents leaving the junction are 18 A and 4 A. What is the value of the fifth current?
Solution:
15 A +5 A + 3 A = 18 A + 4 A +I5
I5 =23 A – 22 A
I5 =1 A
Answer : Value of fifth current is 1 A
Question-2
In a circuit, three wires meet at a junction. The currents entering the junction are 6 A and 4 A and the currents leaving the junction are 8 A. What is the value of the fourth current?
Solution:
Sum of the input current = sum of the output current
6 A + 4 A = 8 A + I4
I4 A =10 A – 8 A
I4 =2 A
Answer : Value of fourth current is 2 A
Question- 3
In a circuit three wires meet at a junction.The currents entering the junction are 5 A and 3 A and the current leaving the junction is 7 A. If the direction of 3A is reversed. What is the new value of the fourth current?
Solution:
Initially
Sum of the input current = sum of the output current
5 A + 3 A = 7 A + I4
I4 = 1 A
When the direction of current 3 A is reversed
5 A = 10A+I4
I4 = – 5 A
The negative sign indicates the direction of the fourth current is opposite to the assumed direction.
Question- 4
In a circuit two junctions A and B are connected. At junction A the current entering are 8 A and 4 A and the current leaving is 10 A. At the junction B, the currents entering are 6 A and 2 A, and the current leaving is 7 A. What is the current flowing between the junctions A and B.
Solution:
At the junction A
Sum of the input current = sum of the output current
8 A + 4 A = 10 A + IAB
IAB = 2 A
At the junction B
6 A + 2A + IAB = 7 A+IBA
IBA = 10 A – 7A
I BA = 3 A
Current flowing between the junction A and B is 2 A
Question- 5
In a household circuit three appliances are connected in parallel.The current drawn by the appliances are 3A, 4A and 5A. What is the total current supplied by the power line.?
Solution:
Total input current = Total output current
I total = 3 A+ 4 A +5 A = 12 A
Answer 12 A
Kirchhoff’s First law:Frequently Asked Questions (FAQ) and Answers
- What is Kirchhoff’s first law?
Answer:
- Kirchhoff’s first law states that “IN AN ELECTRIC CIRCUIT, THE ALGEBRAIC SUM OF CURRENT AT ANY JUNCTION IS ZERO”.TOTAL CURRENT ENTERING A JUNCTION EQUALS TOTAL CURRENT LEAVING THE JUNCTION.Current flowing towards the junction is taken as POSITIVE and current flowing away from the junction is taken as NEGATIVE.
- What is the significance of Kirchhoff’s first law?
Answer:
- To determine unknown currents in circuits, Designing and troubleshooting electrical and electronic systems, To analyze complex circuits with multiple branches and junctions.
- How is Kirchhoff’s first law applied in circuit analysis?
Answer:
- Refer to the above images.
- Can Kirchhoff’s first law be applied to a closed loop?
Answer : No, Applied only at junctions.
- What happens if the assumed direction of current is wrong?
Answer:
- Calculated value of the current will be negative.
- How is Kirchhoff’s first law related to conservation of charge?
Answer:
- This law is based on LAW OF CONSERVATION OF CHARGES.This law is widely used in electrical engineering.The current law relies on the fact that the net charge in the wires and components is constant.
- What are the limitations of Kirchhoff’s first law?
Answer:Valid only for lumped circuits(Where the size of the circuit is smaller than the wavelength of the signals),It does not account for the energy losses due to radiation.
- Give an example of Kirchhoff’s first law in a parallel circuit
Answer: The total current (I) from the battery splits into individual currents(I1, I2, I3) through the resistors.
- How does Kirchhoff’s first law apply to a series circuit?
Answer:
- In a series circuit, Kirchhoff’s current law is satisfied in the context that current is the same at every point in the circuit.
- What is the difference between Kirchhoff’s first law and Ohm’s law?
Answer:
- Kirchhoff’s current law is used for analyzing current distribution in circuits,Ohm’s law is used to calculate voltage, current or resistance in individual components.
- Can Kirchhoff’s first law be applied to AC circuits?
Answer:
- Yes. It must be applied to the instantaneous values of current.
- What is the practical application of Kirchhoff’s first law?
Answer:
- Household wiring (Check the above numerical).
- How do you handle a circuit with multiple junctions?
Answer:
- Apply Kirchhoff’s current law to each junction,write equations for all junctions then solve the system of equations to find unknown currents.
- What is the mathematical form of Kirchhoff’s first law?
Answer: For the mathematical form refer to the above images.
- Can Kirchhoff’s first law be applied to nonlinear circuits?
Answer: Yes, as long as currents are defined at the junctions.
CONCLUSION
Kirchhoff’s laws, which are based on the concept of charge and energy conservation, allow us to understand and anticipate the behavior of electrical circuits.Kirchhoff’s laws are useful tools for electrical engineers and other professionals who work with circuits.These rules are employed in the solution of complicated circuit issues and the design of electrical systems.
- Kirchhoff’s laws are used to calculate the current through a resistor (use Kirchhoff’s current law to write an equation that sums the current entering and leaving the resistor),
- voltage across a capacitor (use Kirchhoff’s current law and Kirchhoff’s voltage law to write an equation that sums the voltage drop around the capacitor), and
- power dissipated by a resistor (use Kirchhoff’s current law and Kirchhoff’s voltage law to write an equation that relates the power voltage and the resistance of the resistor and to determine the behavior of a circuit under different conditions.
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