## Thevenins Theorem

**Thevenins Theorem** Assignment Help | **Thevenins Theorem** Homework Help

# Thevenin’s Theorem

According to this theorem if a resistor of R ohms be connected between any two terminals of a linear bilateral network (the circuit which has the same characteristics in either direction such as transmission line then resulting steady state current through resistor will be__V__equal to where V is the p.d. across

RL+R

these two points and R is the resistance of the network measured between these two points.

For understanding this theorem let us consider a circuit (shown in) which consists of a source of e.m.f. E with internal resistance of r Ω connected to an external circuit consisting of resistance of R

_{1}and R

_{2 }ohms in series.

So far as terminals AB across which a resistance of R

_{2 }ohms is connected, the network acts as a source of voltage, say of V volts where V is the voltage across AB before connecting external resistor of R

_{1}ohms.

The resistance of network measured between terminals AB (with source of e.m.f removed leaving its internal resistance in the circuit) is given by the expression

R =

__1__

__=__

__R__

_{2}(R_{1}+r)__1__+

__1__R

_{1}+r+R

_{2}

R

_{1}+r R

_{2}

Now when external resistor of R

_{1}ohms is connected across terminals AB, the network behaves as a source of voltage V volts, the internal resistance of R ohms and current flowing through the resistance R

_{1}is given by the expression

I =

__V__

R+RL

Since V = (

__E__

__) R__

_{2}and R =

__R__

_{2}(R_{1}+r)r+R

_{1}+R

_{2}R

_{1}+R

_{2}+r

__ER__

_{2}__r+R__

_{1}+R_{2}I =

__R__+ RL =

_{2}(R_{1}+r)

__ER__

_{3}__R__

_{1}+R

_{2}+r R

_{2}(R

_{1}+r)+RL(R

_{1}+R

_{2}+r)

The Thevenin’s theorem can be stated as below:

The current in any bilateral circuit element which may be called R

_{1}) in a network is the same as would obtained if R

_{1 }were supplied with a source of voltage V in series with an equivalent resistance R,V being the open circuit voltage at the terminals form which R

_{1 }has been removed and R being the resistance that would be measured at these terminals after all sources have been removed and each has been replaced by its internal resistance.

This theorem is advantageous when we are to determine the current in a particular passive element of a linear bilateral network particularly when it is desired to find the current which flows through a resistor for different values of the later.

For more help in

**Thevenins Theorem**click the button below to submit your homework assignment