According to the theorem of superposition, the response (current) in a circuit is proportional to the stimulus (voltage) that causes it. This is true even if there are multiple sources in a circuit. This theorem can be used to analyze a circuit without resorting to Kirchhoff's rules by considering the currents in the circuit to be the superposition of currents caused by each source independently. In this way the circuit can be analyzed by computing equivalent resistances rather than by using the (sometimes) more cumbersome method of Kirchhoff's rules. Furthermore, with the superposition theorem it is possible to examine how the modification of a source in one part of the circuit will affect the currents in all parts of the circuit without having to use Kirchhoff's rules to recalculate all of the currents. Consider the circuit shown in Fig. If the circuit were redrawn with the 55.0-V and 57.0-V sources replaced by short circuits, the circuit could be analyzed by the method of equivalent resistances without resorting to Kirchhoff's rules, and the current in each branch could be found in a simple manner. Similarly, if the circuit with the 92.0-V and the 55.0-V sources were replaced by short circuits, the circuit could again be analyzed in a simple manner. Finally, if the 92.0-V and the 57.0-V sources were replaced with a short circuit, the circuit could once again be analyzed simply. By superimposing the respective currents found in each of the branches by using the three simplified circuits, we can find the actual current in each branch.
(a) Using Kirchhoff's rules, find the branch currents in the 140.0-Ω, 210.0- Ω, and 35.0- Ω resistors.
(b) Using a circuit similar to the circuit of Fig, but with the 55.0-V and 57.0-V sources replaced by a short circuit, determine the currents in each resistance. (c) Repeat part (b) by replacing the 92.0-V and 55.0-V sources by short circuits, leaving the 57.0-V source intact.
(d) Repeat part (b) by replacing the 92.0-V and 57.0-V sources by short circuits, leaving the 55.0-V source intact.
(e) Verify the superposition theorem by taking the currents calculated in parts (b), (c), and (d) and comparing them with the currents calculated in part (a).

140.0 0 35.0 0 ww 2210.0N 92.0 V. 57.0 V 55.0 V