What is Kirchoff's current law of electric circuit? Calculate the potential difference between A and C from the given figure

Answer
290.7k+ views
Hint:-The Kirchoff’s current law is basically conservation of charge which states that the total current entering and leaving a junction has to be zero.
Apply Kirchoff’s current law at the node C i.e. the sum of all outgoing (or incoming) current is zero.
Also, current $I = \dfrac{{PD}}{R}$ where $PD$ is the potential difference between any two points and $R$ is the resistance between these two points. Remember current flows from higher potential to lower potential.
Complete step-by-step solution:-
The Kirchoff’s current law states that the total current entering a junction or a node is equal to the charge leaving the node.
In other words, the algebraic sum of every current entering and leaving the junction has to be zero. This property of Kirchhoff law is commonly called Conservation of charge.
Now, in the question we are asked to find the potential difference between A and C.
For this, we have to first calculate the absolute potential of point A and point C.
As the voltage of the battery is given as $100V$ and the positive terminal is connected to point A.
So let us take ${V_A} = 110V$ and ${V_B} = 0$
We know that the current flows from higher potential to lower potential. Also, current $I = \dfrac{{PD}}{R}$ where $PD$ is the potential difference between any two points and $R$ is the resistance between these two points.
Therefore we first calculate equivalent resistance between A and C
$40\Omega $ and $20\Omega $ are in series which gives $40\Omega + 20\Omega = 60\Omega $ which is again parallel with $60\Omega $.
So, ${R_{AC}} = \dfrac{{60}}{2} = 30\Omega $ and ${R_{AB}} = 20\Omega $
Now in order to find the potential of point C, we apply Kirchoff’s current law at the node C i.e. the sum of all outgoing (you can also take incoming) current is zero.
$\dfrac{{{V_C} - {V_A}}}{{{R_{AC}}}} + \dfrac{{{V_C} - {V_B}}}{{{R_{AB}}}} = 0$
On substituting the values we have
$\dfrac{{{V_C} - 110}}{{30}} + \dfrac{{{V_C} - 0}}{{20}} = 0$
On simplifying the equation we get
${V_C} = 44\Omega $
Hence, the potential difference between A and C
${V_C} - {V_A} = 110V - 44V = 66V$ . This is the final answer.
Note:- Kirchhoff’s Current Law is also known as Kirchhoff’s First Law or Kirchhoff’s Junction Rule. According to the Junction rule the algebraic sum of the currents into a junction is equal to the sum of currents outside the junction.
The term Node or a junction is just a connection of two or more conductors like cables and other components. Kirchhoff’s current law can also be used to analyze parallel circuits.
Apply Kirchoff’s current law at the node C i.e. the sum of all outgoing (or incoming) current is zero.
Also, current $I = \dfrac{{PD}}{R}$ where $PD$ is the potential difference between any two points and $R$ is the resistance between these two points. Remember current flows from higher potential to lower potential.
Complete step-by-step solution:-
The Kirchoff’s current law states that the total current entering a junction or a node is equal to the charge leaving the node.
In other words, the algebraic sum of every current entering and leaving the junction has to be zero. This property of Kirchhoff law is commonly called Conservation of charge.
Now, in the question we are asked to find the potential difference between A and C.
For this, we have to first calculate the absolute potential of point A and point C.
As the voltage of the battery is given as $100V$ and the positive terminal is connected to point A.
So let us take ${V_A} = 110V$ and ${V_B} = 0$
We know that the current flows from higher potential to lower potential. Also, current $I = \dfrac{{PD}}{R}$ where $PD$ is the potential difference between any two points and $R$ is the resistance between these two points.
Therefore we first calculate equivalent resistance between A and C
$40\Omega $ and $20\Omega $ are in series which gives $40\Omega + 20\Omega = 60\Omega $ which is again parallel with $60\Omega $.
So, ${R_{AC}} = \dfrac{{60}}{2} = 30\Omega $ and ${R_{AB}} = 20\Omega $
Now in order to find the potential of point C, we apply Kirchoff’s current law at the node C i.e. the sum of all outgoing (you can also take incoming) current is zero.
$\dfrac{{{V_C} - {V_A}}}{{{R_{AC}}}} + \dfrac{{{V_C} - {V_B}}}{{{R_{AB}}}} = 0$
On substituting the values we have
$\dfrac{{{V_C} - 110}}{{30}} + \dfrac{{{V_C} - 0}}{{20}} = 0$
On simplifying the equation we get
${V_C} = 44\Omega $
Hence, the potential difference between A and C
${V_C} - {V_A} = 110V - 44V = 66V$ . This is the final answer.
Note:- Kirchhoff’s Current Law is also known as Kirchhoff’s First Law or Kirchhoff’s Junction Rule. According to the Junction rule the algebraic sum of the currents into a junction is equal to the sum of currents outside the junction.
The term Node or a junction is just a connection of two or more conductors like cables and other components. Kirchhoff’s current law can also be used to analyze parallel circuits.
Last updated date: 04th Jun 2023
•
Total views: 290.7k
•
Views today: 3.46k
Recently Updated Pages
Most eubacterial antibiotics are obtained from A Rhizobium class 12 biology NEET_UG

Salamin bioinsecticides have been extracted from A class 12 biology NEET_UG

Which of the following statements regarding Baculoviruses class 12 biology NEET_UG

Sewage or municipal sewer pipes should not be directly class 12 biology NEET_UG

Sewage purification is performed by A Microbes B Fertilisers class 12 biology NEET_UG

Enzyme immobilisation is Aconversion of an active enzyme class 12 biology NEET_UG

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE
