Kirchoff’s Law – Physics Notes – For W.B.C.S. Examination.

কির্চফের আইন – পদার্থবিজ্ঞানের নোট – WBCS পরীক্ষা।

Kirchhoffs Current Law or KCL, states that the “total current or charge entering a junction or node is exactly equal to the charge leaving the node as it has no other place to go except to leave, as no charge is lost within the node“. In other words the algebraic sum of ALL the currents entering and leaving a node must be equal to zero, I_(exiting) + I_(entering) = 0. This idea by Kirchhoff is commonly known as the Conservation of Charge.Continue Reading Kirchoff’s Law – Physics Notes – For W.B.C.S. Examination.

Kirchhoffs Current Law

Here, the three currents entering the node, I₁, I₂, I₃ are all positive in value and the two currents leaving the node, I₄ and I₅ are negative in value. Then this means we can also rewrite the equation as;

I₁ + I₂ + I₃ – I₄ – I₅ = 0

The term Node in an electrical circuit generally refers to a connection or junction of two or more current carrying paths or elements such as cables and components. Also for current to flow either in or out of a node a closed circuit path must exist. We can use Kirchhoff’s current law when analysing parallel circuits.

Kirchhoffs Second Law – The Voltage Law, (KVL)

Kirchhoffs Voltage Law or KVL, states that “in any closed loop network, the total voltage around the loop is equal to the sum of all the voltage drops within the same loop” which is also equal to zero. In other words the algebraic sum of all voltages within the loop must be equal to zero. This idea by Kirchhoff is known as the Conservation of Energy.

Kirchhoffs Voltage Law

Starting at any point in the loop continue in the same direction noting the direction of all the voltage drops, either positive or negative, and returning back to the same starting point. It is important to maintain the same direction either clockwise or anti-clockwise or the final voltage sum will not be equal to zero. We can use Kirchhoff’s voltage law when analysing series circuits.

When analysing either DC circuits or AC circuits using Kirchhoffs Circuit Laws a number of definitions and terminologies are used to describe the parts of the circuit being analysed such as: node, paths, branches, loops and meshes. These terms are used frequently in circuit analysis so it is important to understand them.

Common DC Circuit Theory Terms:

• • Circuit – a circuit is a closed loop conducting path in which an electrical current flows.
• • Path – a single line of connecting elements or sources.
• • Node – a node is a junction, connection or terminal within a circuit were two or more circuit elements are connected or joined together giving a connection point between two or more branches. A node is indicated by a dot.
• • Branch – a branch is a single or group of components such as resistors or a source which are connected between two nodes.
• • Loop – a loop is a simple closed path in a circuit in which no circuit element or node is encountered more than once.
• • Mesh – a mesh is a single open loop that does not have a closed path. There are no components inside a mesh.

  Using Kirchhoffs Current Law, KCL the equations are given as:

  At node A :    I₁ + I₂ = I₃

  At node B :    I₃ = I₁ + I₂

  Using Kirchhoffs Voltage Law, KVL the equations are given as:

  Loop 1 is given as :    10 = R₁ I₁ + R₃ I₃ = 10I₁ + 40I₃

  Loop 2 is given as :    20 = R₂ I₂ + R₃ I₃ = 20I₂ + 40I₃

  Loop 3 is given as :    10 – 20 = 10I₁ – 20I₂

  As I₃ is the sum of I₁ + I₂ we can rewrite the equations as;

  Eq. No 1 :    10 = 10I₁ + 40(I₁ + I₂)  =  50I₁ + 40I₂

  Eq. No 2 :    20 = 20I₂ + 40(I₁ + I₂)  =  40I₁ + 60I₂

  We now have two “Simultaneous Equations” that can be reduced to give us the values of I₁ and I₂

  Substitution of I₁ in terms of I₂ gives us the value of I₁ as -0.143 Amps

  Substitution of I₂ in terms of I₁ gives us the value of I₂ as +0.429 Amps

  As :    I₃ = I₁ + I₂

  The current flowing in resistor R₃ is given as :    -0.143 + 0.429 = 0.286 Amps

  and the voltage across the resistor R₃ is given as :    0.286 x 40 = 11.44 volts

  The negative sign for I₁ means that the direction of current flow initially chosen was wrong, but never the less still valid. In fact, the 20v battery is charging the 10v battery.

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