Kirchhoff First Law: Junction Rule, Current Law and Nodal Rule

Kirchhoff First Law

Edited By Vishal kumar | Updated on Jul 02, 2025 05:34 PM IST

Kirchhoff's first law states that the algebraic sum of the currents meeting at a point in an electrical circuit is always zero. It is also called the junction rule. This law is based upon the fact that in an electrical circuit, a point can neither act as a source of charge nor the charge accumulate at that point.

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What is Kirchoff's First Law?
Solved Examples Based on Kirchoff's First Law
Summary

Kirchhoff First Law

In this article, we will discuss the working conditions of Kirchhoff's first law. it helps us analyze and solve complex circuits by ensuring the conservation of electric charge and solving some important examples related to Kirchoff's first law. It is an important concept of current electricity for those who are preparing for class 12, NEET and JEE Main exams. Over the last ten years of the JEE Main exam (from 2013 to 2023), a total of three questions have been asked on this concept. And for NEET one question was asked from this concept.

What is Kirchoff's First Law?

In a circuit, at any junction, the sum of the currents entering the junction must equal the sum of the currents leaving the junction. This law is also known as the Junction rule or current law (KCL).

$\sum i = 0$

$i_{1} + i_{3} = i_{2} + i_{4}$

Solved Examples Based on Kirchoff's First Law

Example 1: In the given figure, which of the following relation is correct?

1) $i_{1} + i_{2} - i_{3} + i_{4} - i_{5} - i_{6} + i_{7} = 0$
2) $i_{1} + i_{2} + i_{3} - i_{4} - i_{5} + i_{6} - i_{7} = 0$
3) $i_{1} - i_{2} - i_{3} + i_{4} + i_{5} - i_{6} - i_{7} = 0$
4) $i_{1} + i_{2} - i_{3} + i_{4} + i_{5} - i_{6} - i_{7} = 0$

Solution:

In a circuit at any junction, the sum of the currents entering the junction must equal the sum of the currents leaving the junction.

This law is also known as the Junction rule or current law

Total incoming current = Total outgoing current

$\begin{aligned} \Rightarrow i_{1} + i_{4} + i_{5} = i_{2} + i_{3} + i_{6} + i_{7} \\ \Rightarrow i_{1} - i_{2} - i_{3} + i_{4} + i_{5} - i_{6} - i_{7} = 0 \end{aligned}$

Hence, the answer is option (3).

Example 2: The Kirchhoff's first law $(\sum i = 0)$ and second law $(\sum i R = \sum E)$ where the symbols have their usual meanings, are respectively based on-

1) conservation of charge, conservation of energy

2) conservation of charge, conservation of momentum

3) conservation of energy, conservation of charge

4) conservation of momentum, conservation of charge.

Solution:

Kirchoff's first law

$\begin{aligned} \sum i = 0 \\ i_{1} + i_{3} = i_{2} + i_{4} \end{aligned}$

wherein

Kirchhoff's first law $[\sum i = 0]$ is based on conservation of charge
Kirchhoff's second law $[\sum i R = \sum E]$ is based on the conservation of energy.

Hence, the answer is option (1).

Example 3: In the given circuit diagram, the currents, I₁ = -0.3 A, I4 = 0.8 A and I5 = 0.4 A, are flowing as shown. The currents I2 , I3 and I6 ,respectively, are :

1) -0.4 A, 0.4 A, 1.1 A

2) 1.1 A -0.4 A, 0.4 A

3) 0.4 A,1.1 A,0.4 A

4) 1.1 A,0.4 A,0.4 A

Solution:

Apply Kcl at Q

I₆+I₃ = I₁+ I₂ .........(1)

I₁ = 0.3A

I₄ = 0.8A

I₅ = 0.4A

KCL at 5

I₄= I₅ +I₃

I₃ = I₄ - I₅

= 0.8 +0.4

=0.4A

KCL at R

I₁+I₂ = I₄

I₂ = I₄ - I₁

= 0.8 - (-0.3)

=1.1A

From equation (1)

I₆ + I₃ = I₁+ I₂

I₆ = I₁ + I₂ - I₃

= -0.3+1.1 -0.4

=0.4A

I₂ = 1.1A

I₃ = 0.4A

I₆ = 0.4A

Hence, the answer is option (4).

Example 4: When the switch S, in the circuit shown, is closed, then the value of current I (in amperes) will be:

1) 5

2) 3

3) 4

4) 2

Solution:

By KCL

i₁ + i₂ = i

Let voltage at C be V

$\frac{20 - V}{2} + \frac{10 - V}{4} = \frac{V}{2}$

12.5 = 1.25 V

V = 10 volt

$i = \frac{V}{2} = \frac{10}{2} = 5 A$

Hence, the answer is option (1).

Example 5: The value of current in the $6\; \Omega$ resistance is :

1) 4A

2) 8A

3) 10A

4) 6A

Solution:

Applying KCL at the junction with voltage x (assigned)

By KCL,

$\begin{aligned} I_{1} + I_{2} + I_{3} = 0 \\ (\frac{x - 90}{5}) + (\frac{x - 140}{20}) + (\frac{x - 0}{6}) = 0 \\ 24 x - 24 \times 90 + 6 x - 6 \times 140 + 20 x = 0 \\ 50 x = 24 \times 90 + 6 \times 140 \\ = 6 [4 \times 90 + 140] \\ 50 x = 3000 \\ x = 60 V \end{aligned}$

Current through the resistor is

$I_{3} = (\frac{x - 0}{6}) = (\frac{60 - 0}{6}) = 10 A$

Hence, the answer is option (3).

Summary

Kirchhoff's First Law, which is also called the Current Law, says that the sum of all currents going into any point of a circuit (or junction) is equal to the sum of all currents leaving it. It’s founded on the principle of conservation of electric charge - no charge can either be created or destroyed at these points. By applying the principles of Kirchhoff's First Law it is possible to determine unknown currents and analyze circuit electricity flow in circuits that are complex.

Frequently Asked Questions (FAQs)

1. Kirchoff's first law works on which principle?

Kirchoff's first law works on the conservation of charge principle

2. Can Kirchhoff's First Law be used for both AC and DC circuits?

Yes, this law is used for both AC and DC.

3. What is a junction in the context of Kirchhoff's First Law?

A junction, or node, is a point in a circuit where three or more conductors meet, allowing current to flow in and out.

4. How is Kirchhoff's First Law applied in circuit analysis?

To apply KCL, you identify nodes (points where multiple branches connect) in a circuit. Then, you write equations based on the currents entering and leaving each node. These equations are solved simultaneously with other circuit equations to find all unknown currents and voltages.

5. What is Kirchhoff's First Law?

Kirchhoff's First Law, also known as Kirchhoff's Current Law (KCL), states that the total current entering a junction or node in an electrical circuit is equal to the total current leaving that junction. This law is based on the principle of conservation of charge.

6. How does Kirchhoff's First Law relate to conservation of charge?

Kirchhoff's First Law is a direct application of the conservation of charge principle. It ensures that charge is neither created nor destroyed at any point in a circuit. The law implies that charge cannot accumulate at a junction, so the incoming current must equal the outgoing current.

7. Can Kirchhoff's First Law be applied to AC circuits?

Yes, Kirchhoff's First Law applies to both DC and AC circuits. In AC circuits, the law holds true for instantaneous current values at any given moment, even though the current direction may change over time.

8. What happens if the sum of currents at a junction is not zero?

If the sum of currents at a junction is not zero, it would violate the principle of conservation of charge. This situation is physically impossible in a real circuit. Any apparent violation would indicate an error in measurement or calculation.

9. How does Kirchhoff's First Law apply to parallel circuits?

In parallel circuits, Kirchhoff's First Law is particularly useful. It states that the total current entering a parallel junction must equal the sum of currents flowing through each parallel branch. This helps in analyzing current distribution in parallel circuits.

10. Can Kirchhoff's First Law be used to solve complex circuit problems?

Yes, Kirchhoff's First Law is a powerful tool for solving complex circuit problems. It can be applied to multiple junctions in a circuit, creating a system of equations that can be solved to determine unknown currents throughout the circuit.

11. How can Kirchhoff's First Law be used to detect faults in a circuit?

Kirchhoff's First Law can be used to detect faults by measuring currents at various junctions. If the sum of currents at any junction is not zero, it indicates a problem such as a short circuit, open circuit, or faulty component that's causing current leakage.

12. Can Kirchhoff's First Law be used to analyze circuits with non-linear components?

Yes, Kirchhoff's First Law can be applied to circuits with non-linear components. The law itself doesn't depend on the linearity of components. However, solving the resulting equations may require more advanced techniques like numerical methods.

13. How does Kirchhoff's First Law apply to circuits with transformers?

In circuits with transformers, Kirchhoff's First Law applies separately to the primary and secondary sides. The law ensures current balance at each winding, but the current magnitudes may differ between primary and secondary due to the turns ratio.

14. Can Kirchhoff's First Law be used to analyze circuits with current sources?

Yes, Kirchhoff's First Law is particularly useful for analyzing circuits with current sources. It helps determine how the current from the source distributes through different branches of the circuit, ensuring that the total current is conserved at each junction.

15. How does Kirchhoff's First Law apply to circuits with capacitors in parallel?

For capacitors in parallel, Kirchhoff's First Law dictates that the total current entering the parallel combination equals the sum of currents through each capacitor. This helps in analyzing charge distribution among parallel capacitors during charging or discharging.

16. Can Kirchhoff's First Law be used to analyze circuits with multiple power sources?

Yes, Kirchhoff's First Law is particularly useful for circuits with multiple power sources. It helps determine how currents from different sources combine and distribute through the circuit, ensuring overall current balance at each junction.

17. How does Kirchhoff's First Law apply to three-phase electrical systems?

In three-phase systems, Kirchhoff's First Law applies to each phase individually and to the system as a whole. For balanced three-phase systems, the sum of currents in all three phases at any junction should equal zero.

18. How does Kirchhoff's First Law apply to circuits with transistors?

For circuits with transistors, Kirchhoff's First Law applies to each terminal (emitter, base, collector). It helps analyze how current is distributed between these terminals, which is crucial for understanding transistor operation in amplifier and switching applications.

19. Can Kirchhoff's First Law be applied to analyze antenna systems?

While Kirchhoff's First Law is primarily used for circuit analysis, its principle can be extended to antenna systems. It helps in analyzing current distribution along antenna elements, ensuring that the total current entering a junction point equals the current leaving it.

20. Can Kirchhoff's First Law be used to analyze circuits with transmission lines?

Yes, Kirchhoff's First Law can be applied to circuits with transmission lines, but care must be taken. For short lines, it applies directly. For long lines, where propagation delays are significant, the law should be applied considering the distributed nature of currents along the line.

21. What is the role of Kirchhoff's First Law in analyzing switched-mode power supplies?

In switched-mode power supplies, Kirchhoff's First Law is crucial for analyzing current flow during different switching states. It helps in understanding how current is transferred between input, storage elements, and output, ensuring efficient energy transfer.

22. How does Kirchhoff's First Law apply to circuits with distributed parameters?

For circuits with distributed parameters, like long transmission lines, Kirchhoff's First Law applies locally at each point along the line. It ensures that the rate of change of current with distance equals the rate at which charge leaves the line per unit length.

23. How does Kirchhoff's First Law apply to circuits with solar cells?

In circuits with solar cells, Kirchhoff's First Law helps analyze how the photogenerated current distributes through the circuit. It ensures that the current produced by the solar cell equals the sum of currents in connected loads and storage devices.

24. How does Kirchhoff's First Law apply to thermoelectric circuits?

In thermoelectric circuits, Kirchhoff's First Law applies to both electrical and thermal currents. It ensures that the electrical current generated by the Seebeck effect is conserved throughout the circuit, helping in the analysis of thermoelectric generators and coolers.

25. How does Kirchhoff's First Law apply to circuits with piezoelectric elements?

For circuits with piezoelectric elements, Kirchhoff's First Law applies to the electrical current generated by mechanical stress. It helps analyze how this current distributes through the circuit, ensuring conservation of charge even when the current source is mechanically induced.

26. Can Kirchhoff's First Law be used to analyze circuits with supercapacitors?

Yes, Kirchhoff's First Law is applicable to circuits with supercapacitors. It helps in analyzing the rapid charge and discharge currents characteristic of supercapacitors, ensuring that the current entering or leaving the supercapacitor is accounted for in the rest of the circuit.

27. How does Kirchhoff's First Law apply to circuits with optocouplers?

In circuits with optocouplers, Kirchhoff's First Law applies separately to the input (LED) and output (phototransistor) sides. It helps analyze how the input current relates to the output current, considering the optical coupling and the conservation of charge on both sides.

28. What is the difference between a node and a junction in Kirchhoff's First Law?

In the context of Kirchhoff's First Law, a node and a junction are essentially the same thing. Both terms refer to a point in a circuit where two or more circuit elements connect. The law is applied at these points to analyze current flow.

29. How does Kirchhoff's First Law relate to Kirchhoff's Second Law?

While Kirchhoff's First Law deals with currents at a junction, Kirchhoff's Second Law (also known as Kirchhoff's Voltage Law) deals with voltages around a closed loop. Together, these laws form a powerful set of tools for analyzing electrical circuits.

30. Can Kirchhoff's First Law be applied to superconductors?

Yes, Kirchhoff's First Law applies to superconductors. In fact, it's particularly relevant because superconductors have zero resistance, allowing current to flow without loss. The law ensures that charge is conserved even in these unique materials.

31. How does Kirchhoff's First Law apply to charging capacitors?

When a capacitor is charging, Kirchhoff's First Law still holds. The current entering the capacitor equals the rate of charge accumulation on its plates. As the capacitor charges, the current decreases, but at any instant, the incoming and outgoing currents at the junction are equal.

32. What role does Kirchhoff's First Law play in circuit design?

Kirchhoff's First Law is crucial in circuit design as it helps engineers predict and control current flow. It ensures that the current requirements of different components are met and helps in designing current dividers and parallel circuits effectively.

33. Is Kirchhoff's First Law valid for non-electrical systems?

While Kirchhoff's First Law is primarily used in electrical circuits, its principle can be applied to other systems where conservation laws apply. For example, it's analogous to mass conservation in fluid dynamics or traffic flow in transportation networks.

34. How does Kirchhoff's First Law apply to semiconductors?

In semiconductors, Kirchhoff's First Law still applies, but it's important to consider both electron and hole currents. The total current at a junction includes both types of charge carriers, and their sum must equal zero.

35. How does Kirchhoff's First Law relate to power conservation in a circuit?

While Kirchhoff's First Law directly deals with current conservation, it indirectly relates to power conservation. By ensuring current balance at junctions, it contributes to the overall energy balance in the circuit, which is crucial for power conservation.

36. What happens to Kirchhoff's First Law in the presence of electromagnetic fields?

Kirchhoff's First Law remains valid in the presence of electromagnetic fields. However, in situations with rapidly changing fields, additional considerations like displacement current (from Maxwell's equations) may need to be included for a complete analysis.

37. How does Kirchhoff's First Law apply to circuits with inductors?

In circuits with inductors, Kirchhoff's First Law still holds at every instant. While inductors resist changes in current, the law ensures that at any given moment, the current entering an inductor equals the current leaving it, maintaining charge conservation.

38. What is the significance of Kirchhoff's First Law in power distribution systems?

In power distribution systems, Kirchhoff's First Law is crucial for load balancing and fault detection. It ensures that the total current supplied by power sources equals the sum of currents drawn by all loads, helping in efficient power management and identifying line losses.

39. Can Kirchhoff's First Law be applied to circuits with time-varying currents?

Yes, Kirchhoff's First Law applies to circuits with time-varying currents. It holds true at every instant, even if the currents are changing rapidly. This makes it valuable in analyzing AC circuits and transient responses.

40. How does Kirchhoff's First Law relate to the concept of ground in circuits?

The concept of ground in circuits doesn't affect Kirchhoff's First Law. The law applies regardless of ground connections. However, ground points are often chosen as reference nodes when applying the law to simplify circuit analysis.

41. What is the relationship between Kirchhoff's First Law and Ohm's Law?

Kirchhoff's First Law and Ohm's Law are complementary. While Ohm's Law relates voltage, current, and resistance for individual components, Kirchhoff's First Law helps analyze how these currents distribute at circuit junctions, allowing for complete circuit analysis.

42. How does Kirchhoff's First Law apply to circuits with diodes?

In circuits with diodes, Kirchhoff's First Law still applies. However, the non-linear nature of diodes means that current flow may be unidirectional. The law helps analyze how current distributes when diodes are conducting or in reverse bias.

43. What is the importance of Kirchhoff's First Law in battery management systems?

In battery management systems, Kirchhoff's First Law is crucial for monitoring charge and discharge currents. It helps ensure that the current flowing into or out of a battery equals the sum of currents in connected circuits, aiding in accurate state-of-charge calculations.

44. How does Kirchhoff's First Law relate to the concept of virtual ground in op-amp circuits?

In op-amp circuits, the concept of virtual ground doesn't violate Kirchhoff's First Law. The law still applies at the virtual ground point, ensuring that the sum of currents entering and leaving this point is zero, even though the point isn't physically grounded.

45. What is the significance of Kirchhoff's First Law in analyzing circuits with feedback?

In circuits with feedback, Kirchhoff's First Law is essential for understanding how the feedback current combines with the input current. It helps in analyzing the current flow in both the forward and feedback paths, crucial for determining the overall circuit behavior.

46. How does Kirchhoff's First Law apply to circuits with mutual inductance?

In circuits with mutual inductance, Kirchhoff's First Law applies to each coil individually. While the magnetic coupling between coils affects the induced voltages, the law ensures that the current entering each coil equals the current leaving it at any instant.

47. How does Kirchhoff's First Law relate to the concept of superposition in circuit analysis?

Kirchhoff's First Law is compatible with the superposition principle. When analyzing a circuit using superposition, the law is applied separately for each source configuration. The final current distribution is the sum of individual distributions, adhering to the law at each step.

48. Can Kirchhoff's First Law be used to analyze quantum circuits?

While classical Kirchhoff's First Law doesn't directly apply to quantum circuits, analogous principles of charge conservation still hold. In quantum circuits, it's necessary to consider quantum effects and use quantum mechanical descriptions of current flow.

49. What is the importance of Kirchhoff's First Law in analyzing RFID circuits?

In RFID circuits, Kirchhoff's First Law is crucial for understanding current distribution in the antenna and chip. It helps in analyzing how induced currents from the reader's field are distributed, ensuring efficient power transfer and signal processing.

50. Can Kirchhoff's First Law be used to analyze circuits with memristors?

Yes, Kirchhoff's First Law applies to circuits with memristors. While memristors have unique current-voltage characteristics, the law still ensures current conservation at junctions, helping to analyze how memristors interact with other circuit elements.

51. How does Kirchhoff's First Law relate to the concept of impedance matching?

Kirchhoff's First Law is important in impedance matching as it helps analyze current distribution when matching networks are introduced. It ensures that the current flowing from the source is properly divided between the load and matching elements.

52. What is the significance of Kirchhoff's First Law in analyzing circuits with Hall effect sensors?

In circuits with Hall effect sensors, Kirchhoff's First Law helps analyze how the Hall current (perpendicular to the main current) interacts with the primary current flow. It ensures that the total current entering the sensor equals the current leaving it, across all dimensions.

53. What is the role of Kirchhoff's First Law in analyzing electromagnetic interference in circuits?

Kirchhoff's First Law is crucial in analyzing electromagnetic interference (EMI) in circuits. It helps track unexpected current paths created by EMI, ensuring that all currents, including those induced by interference, are accounted for at each junction in the circuit.

54. How does Kirchhoff's First Law apply to circuits with ferromagnetic cores?

In circuits with ferromagnetic cores, such as in transformers or inductors, Kirchhoff's First Law applies to the electrical currents in the windings. While the magnetic properties of the core affect the inductance and coupling, the law ensures that electrical current is conserved at each junction of the windings.