Kirchhoff's current law (KCL)The current entering any junction is equal to the current leaving that junction. i1 + i4 =i2 + i3This law is also called Kirchhoff's first law, Kirchhoff's point rule, or Kirchhoff's junction rule (or nodal rule).The principle of conservation of electric charge implies that:At any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node, or: The algebraic sum of currents in a network of conductors meeting at a point is zero. Recalling that current is a signed (positive or negative) quantity reflecting direction towards or away from a node, this principle can be stated as:

n is the total number of branches with currents flowing towards or away from the node.This formula is valid for complex currents:

The law is based on the conservation of charge whereby the charge (measured in coulombs) is the product of the current (in amperes) and the time (in seconds).

UsesA matrix version of Kirchhoff's current law is the basis of most circuit simulation software, such as SPICE.

Q1. Find the current flowing in the 40Ω Resistor, R3

The circuit has 3 branches, 2 nodes (A and B) and 2 independent loops.Using Kirchoffs Current Law, KCL the equations are given as;At node A : I1 + I2 = I3

At node B : I3 = I1 + I2

Using Kirchoffs Voltage Law, KVL the equations are given as;Loop 1 is given as : 10 = R1 x I1 + R3 x I3 = 10I1 + 40I3

Loop 2 is given as : 20 = R2 x I2 + R3 x 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 value of both I1 and I2 Substitution of I1 in terms of I2 gives us the value of I1 as -0.143 AmpsSubstitution of I2 in terms of I1 gives us the value of I2 as +0.429 AmpsAs : I3 = I1 + I2

The current flowing in resistor R3 is given as : -0.143 + 0.429 = 0.286 Ampsand the voltage across the resistor R3 is given as : 0.286 x 40 = 11.44 voltsThe 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.

Kirchhoff's voltage law (KVL)The sum of all the voltages around the loop is equal to zero. v1 + v2 + v3 - v4 = 0This law is also called Kirchhoff's second law, Kirchhoff's loop (or mesh) rule,

andKirchhoff's second rule.The principle of conservation of energy implies thatThe directed sum of the electrical potential differences (voltage) around any closed network

is zero, or:More simply, the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop, or:The algebraic sum of the products of the resistances of the conductors and the currents in them in a closed loop is equal to the total emf available in that loop.Similarly to KCL, it can be stated as:

Here, n is the total number of voltages measured. The voltages may also be complex:

This law is based on the conservation of energy whereby voltage is defined as the energy per unit charge. The total amount of energy gained per unit charge must equal the amount of energy lost per unit charge. The conservation of energy states that energy cannot be created or destroyed; it can only be transformed from one form to another.