Kirchoff's rule - definition, Practice problems, FAQs

Your physics teacher assigns you a task: take a couple of resistors, three batteries, and make a circuit. A closed circuit can be constructed using the above; but there’s a problem: current and voltage difference between any two points are hard to determine, since there are multiple values of current and resistances. Kirchoff’s laws help solving problems related to complex circuits; the law can not only be applied for resistors; but a circuit containing capacitors, resistors or other electrical elements as well. They were coined by Gustav Robert Kirchoff, a German physicist born on March 12, 1824, born in Konigsberg, in Russia. He coined two laws- both are named after him as Kirchhoff’s first law and Kirchoff’s second law. Apart from his contributions to electrical engineering, Kirchoff has also contributed to black body radiation. In this article, we will explore Kirchoff’s rule in detail.

Table of contents

• Kirchhoff’s current law
• Kirchhoff’s voltage law
• Practice problems
• FAQs

Kirchoff’s current law

Kirchoff’s Current law (KCL) is also called the Nodal law or Junction Law.

The current entering a junction current leaving.

The current entering a junction current leaving

             Fig showing currents flowing across a node

From the above diagram, currents are entering the junction, currents leave the junction. Then according to KCL,

KCL is based on the law of conservation of charge.

At the junction:

But current  

Sum of charges entering the node Sum of charges leaving the node

Kirchoff’s voltage law:

According to Kirchoff’s voltage law(KVL), the algebraic sum of all the potential differences while traversing along a closed loop is zero. It is a consequence of the Law of Conservation of energy.

             Current flowing in a circuit

Along the closed loop , going in the clockwise direction, we find that the current also flows in the clockwise direction. So,

 +

Going in the anticlockwise direction, along , current flows along clockwise direction, so

Both equations and are the same 

Video explanation

https://www.youtube.com/watch?v=DHAHG_uDufM&t=5022s

Practice problems

1) In the circuit shown below, calculate the current in the resistor ? 

(a) , from to (b) , from to (c) (d) , from to

A. b

Currents flow as shown. 

Applying KCL at junction

Applying KVL in loop

Applying KVL along loop

Solving equations and , we get

Hence the current flowing in will be from to

2) In the circuit shown, the cells and have negligible resistances. , and . There’s no deflection in the galvanometer. The value of is 

(b) (c) (d)

Solution) b

Given ,

Applying Kirchoff’s Voltage law in loop , we get,

is the current flowing in resistances and

Applying Kirchoff’s Voltage law in loop ,

Given, current flowing through the galvanometer,

3) In the following circuit, if determine the electric current that flows in the circuit below.

Solution ) Let be the current flowing in the circuit. Assuming direction of current is also clockwise, applying KVL, 

Substituting the values in the equation, we get

=

=

4) Determine the electric current that flows in the circuit shown in the figure below.

Solution)

In the above circuit, assuming direction of current flow to be clockwise, applying KVL, 

we get

sign in the current indicates that the direction of current is anti-clockwise opposite to the assumed direction.

FAQs:

Q. Kirchoff’s current law is a consequence of conservation of charge. Why?
Ans. It states that the current entering a node current leaving a node. 

Since current = charge/time. For a given time, charge entering a node charge leaving a node. Hence, it is based on the law of conservation of charge.

Q. Write the equation for work done when a charge is accelerated through a potential difference
Ans. Work done,  

Q. Write the equation for currents and at a junction when currents and are entering a junction and is leaving the junction.
Ans: The current entering a junction current leaving.

Q. What does a negative current mean?
Ans: It means that the actual current in the circuit is in the opposite direction of our assumed current direction.