Kirchoff’s Voltage and current laws

Kirchoff’s Voltage and current laws


Kirchoff’s Circuit Law


                         We have seen that most linear circuits obey Ohm’s Law. However, sometimes in complex circuits such as bridge or T networks, we can not simply use Ohm’s Law alone to find the voltage or current circulating within the circuit. For such types of calculations, we need certain rules, which allow us to obtain the circuit equations and for this we may use Kirchoff’s Circuit Law.

In 1845, a German physicist, Gustav Kirchoff postulated a pair of  laws to deal with the conservation of current and energy within electrical circuits. These two rules are commonly known as: Kirchoff’s Circuital Laws. One of the Kirchoff laws dealing with the current flowing around a closed circuit, Kirchoff’s Current Law, (KCL) while the other law deals with the voltage sources present in a closed circuit, Kirchoff’s Voltage Law, (KVL).

Kirchoff’s  Current Law, (KCL)

Kirchoff’s 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 Kirchoff is commonly known as the Conservation of Charge.

Kirchoff’s Current Law

Kirchoffs Current Law

Here, the 3 currents entering the node, I1, I2, I3 are all positive in value and the 2 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 Kirchoff’s current law when analyzing parallel circuits.

Kirchoff’s Second Law – The Voltage Law, (KVL)

Kirchoff’s 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 Kirchoff is known to be as the Conservation of Energy.

Kirchoff’s Voltage Law

Kirchoffs 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 Kirchoff’s voltage law when analyzing series circuits.


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