“Kirchhoff's Rules”

Abdulrajab Layagin

Who is Gustav Kirchhoff? A German physicist

who contributed to the fundamental understanding of electrical circuits.

He lived between

(12March 1824 –

17October 1887)

Works of Gustav Kirchhoff

Law of Thermal Radiation (1859).

Three Laws of Spectroscopy.

Law of Thermochemistry (1858).

The Kirchhoff’s rules:

Junction Rule:

The algebraic sum of all currents flowing into the junction equals the algebraic sum of all currents flowing out.

= => - = 0

We define a junction as a point in the circuit where three or more conductors meet.

Loop Rule:

The algebraic sum of all potential differences in any loop including those associated with emf’s and resistive elements must be equal to zero.

= 0

A loop is any closed conducting path.

Sign Convention for Kirchhoff’s Loop Rule:

Travel Travel

ԑ ԑ - + - +

Travel Travel

R R

+ - -IR - + +IR

I I

General procedure for analyzing a circuit using Kirchhoff's: Replace any combination of resistors

in series or parallel with their equivalent resistance.

Label each remaining resistor and each emf with a symbol.

Choose a direction for the current in each branch of the circuit, and label each current.

Add plus and minus signs to label the high and low potential sides of each circuit element, (i.e. each emf, resistor, capacitor).

Label the side of the resistor on which the current enters with a plus sign (+) and the side on which the current exits with a minus sign (-).

Apply Kirchhoff's first rule to all but one of the junctions in the circuit.

Apply Kirchhoff's second rule to as many loops as needed to obtain as many equations (including the junction equations) as you have unknowns.

Solve the equations to obtain the values of the unknowns.

Example

1. Neglecting the internal resistances of the batteries, find the currents in the branches of the circuit as shown in figure 1.

Figure 1 12V 8V

a

3Ω 4Ω 5Ω

b

Exercise:

1. (a) Write Kirchhoff’s rules for two loops and one junction for the circuit shown in figure 2.

(b) Solve the equation for the current in each branch of the circuit when

= 24V = 10Ω

= 12V = 20Ω

= 50Ω = 25Ω

Figure 2

End

Thank You!!!!