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Kirchhoff's Laws | Physics Class 12 - NEET PDF Download

In this document, we'll explore Kirchhoff's laws, which are two sets of rules about the flow of electricity in circuits. These laws talk about current (the flow of electricity) and potential difference (or voltage) in electrical circuits. They were first explained by a German physicist named Gustav Kirchhoff in 1845. Kirchhoff's laws build upon the ideas of Georg Ohm and came before the work of James Clerk Maxwell. These laws are widely used in electrical engineering and are sometimes simply called Kirchhoff's rules. They are crucial for analyzing networks of electrical components and can be applied to understand how circuits behave over time and at different frequencies. 

What are Kirchhoff's law? 

Kirchhoff's Laws are two fundamental principles used in the analysis of electrical circuits, named after the German physicist Gustav Kirchhoff. These laws are crucial for understanding and solving complex circuits.

Kirchhoff`s LawsKirchhoff's Laws

Two fundamental principles for analyzing electrical circuits: 

Kirchhoff's Voltage Law (KVL)

This law states that in any closed loop within an electrical circuit, the sum of the voltages across all elements (resistors, capacitors, etc.) must equal zero. In other words, the algebraic sum of the voltage drops and rises around a closed loop is always zero. KVL is based on the principle of conservation of energy.

Sign Conventions for Circuit Analysis

Before moving on to the statement of Kirchhoff's law, there are state some sign conventions to be followed in circuit analysis :

(a) The direction of conventional current is from high potential to low potential terminal.

(b) If we traverse from point A to B, there is a drop of potential; similarly, from B to A, there is a gain of potential. If a source of emf is traversed from negative to positive terminal, the change in potential is +E.
  Kirchhoff`s Laws | Physics Class 12 - NEETKirchhoff`s Laws | Physics Class 12 - NEET

(c) While discharging, current is drawn from the battery, and the current comes out from the positive terminal and enters the negative terminal, while charging the battery, the current is forced from the positive terminal of the battery to the negative terminal. Irrespective of the direction of current through a battery, the sign convention mentioned above holds.

(d) The positive plate of a capacitor is at high potential and the negative plate is at low potential. If we traverse a capacitor from a positive plate to a negative plate, the change in potential is -Q/C
Kirchhoff`s Laws | Physics Class 12 - NEET

  • If we traverse a resistor in the direction of current, the change in potential is -IR.
  • If we traverse a resistor in the direction opposite to the direction of the current, the change in potential is +IR.
    Kirchhoff`s Laws | Physics Class 12 - NEET
  • The positive terminal of the source of emf is at high potential and the negative terminal is at low potential. If we traverse a source of emf from the positive terminal to the negative terminal, the change in potential is -E.
  • If a capacitor is traversed from a negative plate to a positive plate, the change in potential is Q/C

Question for Kirchhoff's Laws
Try yourself:
What is Kirchhoff's Voltage Law (KVL)?
View Solution

Kirchhoff's Voltage Law OR Loop Law

This law is based on the law of conservation of energy. Kirchhoff's voltage law (KVL) states that the algebraic sum of the potential difference around any closed loop of an electric circuit is zero.  
  • The KVL reflects that electric force is conservative, the work done by a conservative force on a charge taken around a closed path is zero.
  • We can move clockwise or anticlockwise, it will make no difference because the overall sum of the potential difference is zero.
  • We can start from any point on the loop, we just have to finish at the same point.
  • An ideal battery is modeled by an independent voltage source of emf E and an internal resistance r as shown in Figure. A real battery always absorbs power when there is a current through it, thereby offering resistance to the flow of current.
    Kirchhoff`s Laws | Physics Class 12 - NEET

Kirchhoff's Current Law (KCL)

KCL states that the total current entering a junction or node in an electrical circuit must equal the total current leaving that junction. In mathematical terms, the sum of currents entering a node equals the sum of currents leaving the node. KCL is based on the principle of conservation of charge.

Kirchhoff`s Current LawKirchhoff's Current Law

Here, we have to decide whether the electric currents, represented by Ik, are positive or negative. Imagine a junction where currents either come together or split apart. We're establishing a rule that if we consider one direction as positive, then the other direction is automatically considered negative (and vice versa). It doesn't matter which one we choose as positive or negative, but once we decide on a specific junction, we must stick to that decision for all currents at that junction.

Applications of KCL in Circuits

Writing an Equation for Junction/ Node in the Circuit:

Consider a point or junction O in an electrical circuit. Let I1, and I3 be the currents entering point O and I2, I4, and I5 be the current leaving point O. 

Kirchhoff`s Laws | Physics Class 12 - NEET

Then, according to KCL, the algebraic sum of the current entering and leaving the junction is zero. So apply KCL to junction O. 

According to Kirchhoff’s first law, 

I1 + I3 = I2 + I4 + I5  

The above equation can also be written as,

 I1 + I3 + (–I2 ) + (–I4 ) + (–I5 ) = 0; I1 + I3 – I2 – I4 – I5 = 0 (i.e.  ∑Ik=0 )

Question for Kirchhoff's Laws
Try yourself:
Which law of Kirchhoff's is based on the law of conservation of energy?
View Solution

Solved Examples

Q1: Kirchhoff`s Laws | Physics Class 12 - NEET
In the  figure shown, the current in the  10 V battery is close to :    [Sep. 06, 2020 (II)]
(a) 0.71 A from positive to negative terminal
(b) 0.42 A from positive to negative terminal
(c) 0.21 A from positive to negative terminal
(d) 0.36 A from negative to positive terminal
Ans: 
(c)
Sol:

Kirchhoff`s Laws | Physics Class 12 - NEET 
Using Kirchoff's loop law in loop ABCD
Kirchhoff`s Laws | Physics Class 12 - NEET
Using Kirchoff's loop law in loop BEFC

Kirchhoff`s Laws | Physics Class 12 - NEET

Multiplying equation (i) by 10, we have

Kirchhoff`s Laws | Physics Class 12 - NEET

Multiplying equation (ii) by 17, we have

Kirchhoff`s Laws | Physics Class 12 - NEET

On solving equations (iii) and (iv), we get

Kirchhoff`s Laws | Physics Class 12 - NEET

i1 is negative it means current flows from positive to negative terminal.


Q2: Four resistances 40 Ω, 60 Ω, 90 Ω and 110 Ω make the arms of a quadrilateral ABCD. Across AC is a battery of emf 40 V and internal resistance negligible. The potential difference across BD in V is __________.

Kirchhoff`s Laws | Physics Class 12 - NEET


Sol:

Kirchhoff`s Laws | Physics Class 12 - NEET

Kirchhoff`s Laws | Physics Class 12 - NEET
Kirchhoff`s Laws | Physics Class 12 - NEET

Q3: In the circuit shown, the current in the 1W resistor is:     [2015]
Kirchhoff`s Laws | Physics Class 12 - NEET

(a) 0.13 A, from Q to P
(b) 0.13 A, from P to Q
(c) 1.3 A from P to Q
(d) 0 A
Ans: (a)
Sol:
From KVL
Kirchhoff`s Laws | Physics Class 12 - NEET
Kirchhoff`s Laws | Physics Class 12 - NEET
On solving (1) and (2)
I1 = 0.13A

Direction Q to P, since I1 > I2.

Q4: A 5V battery with internal resistance 2W and a 2V battery with internal resistance 1W are connected to a 10W resistor as shown in the figure.    [2008]
Kirchhoff`s Laws | Physics Class 12 - NEET

The current in the  10Ω  resistor is
 (a) 0.27 A P2 to P1 
(b) 0.03 A P1 to P2 
(c) 0.03 A P2 to P1 
(d) 0.27 A P1 to P2
Ans: (c)
Sol: Applying Kirchoff’s second law in AB P2P1A, we get
Kirchhoff`s Laws | Physics Class 12 - NEET

Kirchhoff`s Laws | Physics Class 12 - NEET

Again applying Kirchoff's second law in P2 CDP1P2 we get,Kirchhoff`s Laws | Physics Class 12 - NEET

Q5: Calculate the current I3 in the circuit below:

Kirchhoff`s Laws | Physics Class 12 - NEET

Sol:
At node or junction C, applying KCL:

Current entering at C=Current leaving from C 

I1+I3=I2 

1A+I3=2A

I3=2-1=1A

Q6: 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:                                                                   (JEE Mains, 2019)

Kirchhoff`s Laws | Physics Class 12 - NEET

Sol: 
Kirchhoff`s Laws | Physics Class 12 - NEET

Q7: When the switch S, in the circuit shown, is closed then the value of current  will be:     

(JEE Mains, 2020)

Kirchhoff`s Laws | Physics Class 12 - NEET

Sol:

Kirchhoff`s Laws | Physics Class 12 - NEET

The document Kirchhoff's Laws | Physics Class 12 - NEET is a part of the NEET Course Physics Class 12.
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FAQs on Kirchhoff's Laws - Physics Class 12 - NEET

1. What is Kirchhoff's Voltage Law (KVL)?
Ans. Kirchhoff's Voltage Law states that the total voltage around a closed loop in a circuit is equal to the sum of the voltage drops within that loop.
2. How is Kirchhoff's Current Law (KCL) applied in circuits?
Ans. Kirchhoff's Current Law states that the total current entering a junction in a circuit is equal to the total current leaving the junction. It is applied to analyze current flow in complex circuits.
3. What are some applications of KCL in circuits?
Ans. KCL is commonly used in circuit analysis to determine unknown currents in different branches of a circuit, to calculate node voltages, and to verify the accuracy of circuit calculations.
4. Can you provide a solved example of Kirchhoff's Laws in a circuit?
Ans. A solved example could involve calculating the voltage drops across different resistors in a circuit using KVL and determining the currents in various branches of the circuit using KCL.
5. What are some frequently asked questions (FAQs) related to Kirchhoff's Laws in exams like JEE?
Ans. Some common FAQs related to Kirchhoff's Laws in exams like JEE include understanding how to apply KCL and KVL in complex circuit problems, analyzing circuits with multiple loops and nodes, and determining the voltage and current distribution in a circuit.
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