**Kirchhoff’s Lows**

The most common low that become the origin of almost all the other lows of electrical circuit theory is ohm’s low. We will have a quick notice about that before start.

See the first article : Basic Electrical – Nominal Voltage, Rated Voltage and Operating Voltage

The first article in the series : Voltage and Electrical Potential

**Ohm’s low**

The electrical current flowing through a resistance (linear element) is directly proportional to the voltage applied across it, and inversely proportional to the resistance. This must be in constant temperature.

This is call’s the **Ohms Law **** and it’s the relationship between voltage, current and the resistance of a circuit.**

But this is much simplifier for the T branch and more complex circuit available with several resistance and voltage sources, so for that we have to use different methods to find the values. So Kirchhoff’s lows come in to act.

There are two Kirchhoff’s lows.

- Kirchhoff’s current low
- Kirchhoff’s voltage low

**Kirchhoff’s Current law – Kirchhoff’s First Low (KCL)**

*Total current or charge entering a junction or node is exactly equal to the charge leaving the node, as no charge is lost within the node.*

*In other words, *

Or this can says that the algebraic sum of the currents input and output a node must be equal to zero.

By that I1+I2 – (I4+I5+I6) = 0

There not must be the equal number of incoming currents and out going currents from the node, it can be different.

**Kirchhoff’s Voltage Low – Kirchhoff’s Second Low (KVL)**

*The total voltage around In any closed loop network, the loop is equal to the sum of all voltage drops in the same loop**”* equal to zero.

Say that the algebraic sum of all voltages in the loop must be equal to zero.

Start at any point of the loop and continue in defined direction, counting the positive and negative voltage drops algebraically, and returning back to the same starting point.Going same direction of clockwise or anti-clockwise is important.

In the analysis of DC circuit theory, there are several terms that frequently used. Those are as follows.

**Common DC Circuit Theory Terms:**

- Circuit – a circuit is a closed loop or path of a circuit an electrical current flows.
- Path – a line of electrical elements connected
- Node – A junction, connection or terminal within a circuit which there are two or more elements connected and joined.
- Branch – single or group of components including resistors, voltage sources connecting each other.
- Loop – simple closed path in a circuit which the elements connected in.
- Mesh – A series of loops

Example 1:

Find current *i*3 at the node shown below

i1 and i2 currents are comming into the node and i3 and i4 are going out of the node.

Now applying KCL at the given node.

i1+i2 = i3+i4

Substitute the known quantities

2+9=i3+4

Solve for i3

i3=7 =7 A

Find currents i3 and i4 at the nodes N1 and N2 shown below.

Example No 2:

Find i3 and i4

In this example the current i3 and i4 flow direction is not given. So it should assume i3 flowing out of node N1 and i4 flowing out of node N2 as shown below (in red) and use Kirchhoff’s current law. So if any changers as the assumption of the direction there will be a minus value result in the calculation. So careful when find the minus result of current.

At node N1, i1 flows into N1 and i2 and i3 flow out of N1, hence

i1 = i2 + i3

Substitute by known quantities

55 = 99 + i3

Solve for i3

i3=−4i3=−4

Because i3 is negative, i3 flows into node N1

At node N2, i3 and i5 flows into N2 and i4 flows out of N2, hence

i3+i5 = i4

Substitute by known quantities

−4+10 = i4

Solve for i4

i4=6

because i4 is positive it therefore flows out of node N2

Example 3:

Use Kirchhoff’s Law of Voltage and all possible closed loops to write equations involving voltages in the circuit below and explain the signs of the voltages.

Step 1: Set negative and positive polarities for all emf or voltage sources.

Step 2: From negative to the positive polarity, we set arrows of each voltage..

Step 3: Use KVL to write the equations

so around the loop if arrow in same direction as we selected, it is positive otherwise negative.

Loop

L1“>L1

: The arrow of the voltage source e“>e

e is in the same direction as the loop counted as positive positive. The arrows of voltages VR1“>VR1

and VR2“>VR2, across the resistors, are against the direction and counted as negative.

Kirchhoff’s Law for loop L1“>L1

L1 gives:

e−VR1−VR2=0e−VR1−VR2=0

Loop L2“>L2

L2: The arrows of the voltage VR2“>VR2

VR2 is in the same direction of the loop hence positive. The arrows of voltages VR2“>VR2

VR2, is against the direction of the loop hence negative.

Kirchhoff’s Law for loop L2“>L2

L2 gives:

VR2−VR3=0“>VR2−VR3=0

VR2−VR3=0

Loop L3“>L3

L3: The arrows of the voltage source e“>e

e is in the same direction as the loop hence positive. The arrows of voltages VR1“>VR1

VR1 and VR3“>VR3

VR3, are against the direction of the loop hence negative.

Kirchhoff’s Law for loop L3“>L3

L3 gives:e−VR1−VR3=0“>e−VR1−VR3=0

Team – Newsican

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