Example of Network Theorems - BZU PAGES: Find Presentations, Reports, Student's Assignments and Daily Discussion; Bahauddin Zakariya University Multan

**bonfire** · #1 17-04-2011, 12:36 AM

Example:

In the circuit below,

,

. Find the value of current

when

is

,

, and

. Moreover, find the value for

for the desired current

.

Method 1, conversion
Find

when

. First convert the

composed of

,

and

into a

composed of

,

and

:

Find overall resistance:

Find overall current:

Find currents through

and

(current divider):

Find voltage at points

and

(assuming negative end of voltage source is ground):

Find current

through

:

The same steps can be repeated for

and

. But it is hard to find a value of

given the require current

. Method 2, Thevenin's theorem
Solve the problem using Thevenin's theorem by the following steps:

remove the branch in question from the circuit and treat the rest as a one-port network.
simplify the one-port network by Thevenin's theorem, find the open circuit voltage and the equivalent internal resistance .
put the branch in equation back as the load of the Thevenin equivalent network and find the current/voltage.

Here, we remove

as the load of a network composed of all other resistors

,

and the voltage source

, then apply Thevenin's theorem to find the open-circuit voltage between the two terminals a and b:

and the internal resistance between a and b (with voltage source

short circuit):

Now find current

for different

,
,
,

and when

,

Example 2: The circuit below, often used in some control system, is composed of two voltages, two potentiometers, and a load resistor. Assume

,

, and

. Find the current

through the load resistor

.

Method 1, Superposition theorem
Find

caused by voltage

, and then

caused by voltage

, then get

.

Short circuit . Assume , so that currents through and are, respectively, and (current divider), and .
, current through is , current through is .
. But , we get scaling factor , and .
Short circuit . Assume , so that currents through and are, respectively, and (current divider), and .
, current through is , current through is .
. But , we get scaling factor , and .
Finally, we get the load current:

Method 2, Thevenin's theorem
Remove

, find open-circuit voltage

and equivalent resistance

, then find

.