Kirchhoff's Law - Junction Law, Loop Law, Class 12

Kirchhoff's Law

    Kirchhoff's law is a fundamental principle of current electricity in the NCERT Class 12 physics curriculum. It consists of two main laws: Kirchhoff's Law and Kirchhoff's Voltage Law.

Kirchhoff's First Law

    Kirchhoff's first law, also known as Kirchhoff's Current Law (KCL), states that in an electric circuit, the algebraic sum of current at any junction must be zero.

        `\Sigma I = 0`

    The total current flowing into a junction equals the current flowing out of that junction. This law is called Kirchhoff's First Law or Junction Law.

    Kirchhoff's first law is based on the principle of 'Conservation of Charge'. When currents in a circuit are steady, the amount of charge flowing towards a junction in any time interval must equal the charge flowing away from that junction in the same time interval.

Kirchhoff's Junction Law Diagram

    According to Kirchhoff's junction law 

        `\Sigma I = 0`

        `I_1 + I_2 - I_3 - I_4 + I_5 = 0`

        `I_1 + I_2 + I_5 =  I_3 + I_4 `

Note :

    ✯    The current flowing toward the junction is taken as positive.

    ✯    The current flowing toward the junction is taken as negative.

    ✯    Kirchhoff's junction law (Kirchhoff's first rule) is based on the principle of conservation of electric charge, which implies that charge cannot accumulate at a junction.

Kirchhoff's Second Law

    Kirchhoff's second law, also known as Kifchhoff's loop law applies to any closed electric circuit. It states that the algebraic sum of the electromotive forces and the sum of the product of the current and resistance in each component around any closed loop are equal. Kirchhoff's second law or loop law is based on the conservation of energy.

        `\Sigma E = \Sigma I R`

Sign Convention for Kirchhoff's Second Law

    ✯    The current-resistance (I R) product is taken as negative if the resistor is traversed in the same direction as the assumed current.

    ✯    The IR product is taken as positive if the resistor is traversed in the opposite direction of the assumed terminal.

Sign Convention for Kirchhoff's Second Law

    ✯    The emf of the cell is taken as a positive sign if the direction of traversal is from its negative to the positive terminal.

    ✯    The emf of a cell is taken as a negative sign if the direction of traversal is from its positive to the negative terminal.

Example

        Consider a closed loop to understand Kirchhoff's Second Law.

Closed Circuit for Kirchhoff's Second Law

At point d by the Kirchhoff's First Law

        ` I_3 = I_1 + I_2 `

In the loop adcba by the Kirchhoff's Second Law

        `\epsilon_1 - \epsilon_2 = I_1 R_1 - I_2 R_2`

In the loop defcd by the Kirchhoff's Second Law

        `\epsilon_2 = I_3 R_3 + I_2 R_2`

    By solving these equations we can find electric currents in different branches as well as we can find potential differences across the resistance.

Example: Find electric current I in the given circuit diagram.

By the Junction Law at point A

        `x = 3 - 1.5 `

        `x = 1.5 A`

By the Junction Law at point B

        `y = x - 1`

        `y = 1.5 - 1`

        `y = 0.5 A`

By the Junction Law at point C

        `I = y - 0.25A`

        `I = 0.5A - 0.25A`

        `I = 0.25A `

Important Facts

    ✯    Conservation Principles: Kirchhoff's laws are based on conservation of charge (Current Law) and conservation of energy (Voltage Lae).

    ✯    Current Law: The sum of potential differences around any closed loop is zero.

Conclusion

    Kirchhoff's laws are essential in the NCERT Class 12 physics curriculum, facilitating circuit analysis. Kirchhoff's current law (KCL) ensures the sum of currents at a junction is zero, while Kirchhoff's voltage law (KVL) states the sum of electromotive forces and products of currents and resistances around a loop is zero.

Kirchhoff's Law MCQs

Q.      Kirchhoff's first law is based on which principle?

(1)  Conservation of Energy

(2) Conservation of Mass

(3) Conservation of Charge

(4) Conservation of Momentum

Answer: (3) Conservation of Charge

Q.      What does Kirchhoff's second lsw state?

(1)  The total current in a closed loop is zero.

(2) The sum of all electromotive forces and the sum of the product of current and resistance in a closed loop are equal.

(3) The sum of currents at a junction is zero.

(4) The voltage across a resistor is proportional to the current.

Answer: (2) The sum of all electromotive forces and the sum of the product of current and resistance in a closed loop are equal. 

Q.      Kirchhoff's second law is based on which principle?

(1)  Conservation of Charge

(2) Conservation of Energy

(3) Conservation of Mass

(4) Conservation of Momentum

Answer: (2) Conservation of Energy 

Q.      How is the emf of a cell taken if the direction of traversal is from its negative to positive terminal?

(1)  Positive

(2) Negative 

(3) Zero

(4) It depends on the current

Answer: (1)  Positive

Q.      According to Kirchhoff's first law, what is the equation at a junction if `I_1 = 2 A`, `I_2 = 3 A`,`I_3 = 1 A` and `I_4 = 4 A`?

(1)  `I_1 + I_2 - I_3 - I_4 = 0`

(2) `I_1 - I_2 + I_3 - I_4 = 0`

(3) `I_1 - I_2 - I_3 + I_4 = 0`

(4) `I_1 + I_2 + I_3 - I_4 = 0`

Answer: (1)  `I_1 + I_2 - I_3 - I_4 = 0`

Q.      If the current `I_3` is equal to the sum of currents `I_1` and `I_2` at a junction, what is the value of `I_3` given `I_1 = 3A` and `I_2 = 4A`?

(1)  1 A

(2) 7 A

(3) 12 A

(4) 3.5 A

Answer: (2) 7 A

Q.      What is the formula representing Kirchhoff's current law?

(1)  `\Sigma E = \Sigma I  R`

(2)  `\Sigma V = 0`

(3)  `\Sigma I = 0`

(4)  ` I = \frac{V}{R}`

Answer: (3)  `\Sigma I = 0`

Q.      Kirchhoff's first rule is also known as 

(1)  Voltage Law

(2)  Loop Law

(3)  Current Law

(4)  Junction Law

Answer: (4)  Junction Law

Q.      Kirchhoff's current law (KCL) is primarily used to analyze which aspect of electric circuits? 

(1)  Voltage

(2)  Current

(3)  Resistance

(4)  Power

Answer: (2)  Current

Related Question 

1. Define Kirchhoff's current law(KCL).

2. State Kirchhoff's voltage law (KVL).

3. What principle is Kirchhoff's current law based on?

4. What is the significance of Kirchhoff's voltage law in circuit analysis?

5. Explain the sign convention for Kirchhoff's loop rule regarding the direction of current.

6. Why are Kirchhoff's current and voltage laws essential in electric circuit analysis?

7. Which formula represents Kirchhoff's current law?

8. What is current?

9. What is an electric circuit?

Read More

Chapter  3:  CURRENT ELECTRICITY

PHYSICS NOTES

• Electric Current Definition and Electric Currents in Conductors 
• Ohm’s Law: Definition, Formula, Limitations, Derivation, Diagram, and Deduction of Ohm's Law 
• Drift of Electrons and the Origin of Resistivity
• Resistivity, Resistivity of Various Materials, Temperature Dependence of Resistivity 
• Mobility Formula in terms of Relaxation Time
• Electrical Energy, Power