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
.