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

Answer
342.6k+ 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.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are

Define absolute refractive index of a medium

Why should electric field lines never cross each other class 12 physics CBSE

An electrostatic field line is a continuous curve That class 12 physics CBSE

What are the measures one has to take to prevent contracting class 12 biology CBSE

Suggest some methods to assist infertile couples to class 12 biology CBSE

Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What is pollution? How many types of pollution? Define it

Scroll valve is present in a Respiratory system of class 11 biology CBSE

What is BLO What is the full form of BLO class 8 social science CBSE

is known as the Land of the Rising Sun A Japan B Norway class 8 social science CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

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

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
