Table of contents  
What are Kirchhoff's law?  
Kirchhoff's Voltage Law (KVL)  
Kirchhoff's Voltage Law OR Loop Law  
Kirchhoff's Current Law (KCL)  
Applications of KCL in Circuits  
Solved Examples 
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.
Kirchhoff's Laws
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.
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.
(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
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.
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 Law
Here, we have to decide whether the electric currents, represented by I_{k}, 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.
Consider a point or junction O in an electrical circuit. Let I_{1}, and I_{3} be the currents entering point O and I_{2}, I_{4}, and I_{5} be the current leaving point O.
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,
I_{1} + I_{3} = I_{2} + I_{4} + I_{5}
The above equation can also be written as,
I_{1} + I_{3} + (–I_{2} ) + (–I_{4} ) + (–I_{5} ) = 0; I_{1} + I_{3} – I_{2} – I_{4} – I_{5} = 0 (i.e. ∑I_{k}=0 )
Q1:
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:
Using Kirchoff's loop law in loop ABCD
Using Kirchoff's loop law in loop BEFC
Multiplying equation (i) by 10, we have
Multiplying equation (ii) by 17, we have
On solving equations (iii) and (iv), we get
i_{1} 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 __________.
Sol:
Q3: In the circuit shown, the current in the 1W resistor is: [2015]
(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
On solving (1) and (2)
I_{1} = 0.13A
Direction Q to P, since I_{1} > I_{2}.
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]
The current in the 10Ω resistor is
(a) 0.27 A P_{2} to P_{1}
(b) 0.03 A P_{1} to P_{2}
(c) 0.03 A P_{2} to P_{1}
(d) 0.27 A P_{1} to P_{2}
Ans: (c)
Sol: Applying Kirchoff’s second law in AB P_{2}P_{1}A, we get
Again applying Kirchoff's second law in P2 CDP_{1}P_{2} we get,
Q5: Calculate the current I_{3} in the circuit below:
Sol:
At node or junction C, applying KCL:
Current entering at C=Current leaving from C
I_{1}+I_{3}=I_{2}
1A+I_{3}=2A
I_{3}=21=1A
Q6: In the given circuit diagram, the currents, I_{1} = – 0.3 A, I_{4} = 0.8 A, and I_{5} = 0.4 A, are flowing as shown. The currents I_{2}, I_{3} and I_{6}, respectively, are: (JEE Mains, 2019)
Sol:
Q7: When the switch S, in the circuit shown, is closed then the value of current will be:
(JEE Mains, 2020)
Sol:
105 videos425 docs114 tests

1. What is Kirchhoff's Voltage Law (KVL)? 
2. How is Kirchhoff's Current Law (KCL) applied in circuits? 
3. What are some applications of KCL in circuits? 
4. Can you provide a solved example of Kirchhoff's Laws in a circuit? 
5. What are some frequently asked questions (FAQs) related to Kirchhoff's Laws in exams like JEE? 

Explore Courses for NEET exam
