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 analyse a circuit without resorting to Kirchhoff's rules by consider-
ing the currents in the circuit to be the superposition of currents caused by each source independently. In this way the circuit can be analysed 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. 26.72. If the circuit were redrawn with the $55.0 \mathrm{~V}$ and $57.0 \mathrm{~V}$ sources replaced by short circuits, the circuit could be analysed 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 $92.0 \mathrm{~V}$ and the $55.0 \mathrm{~V}$ sources were replaced by short circuits, the circuit could again be analysed in a simple manner. Finally, if the $92.0 \mathrm{~V}$ and the $57.0 \mathrm{~V}$ sources were replaced with a short circuit, the circuit could once again be analysed 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 $140.0 \Omega, 210.0 \Omega$ and $35.0 \Omega$ resistors. (b) Using a circuit similar to the circuit of Fig. 26.72 , but with the $55.0 \mathrm{~V}$ and $57.0 \mathrm{~V}$ sources replaced by a short circuit, determine the currents in each resistance. (c) Repeat part (b) by replacing the $92.0 \mathrm{~V}$ and $55.0 \mathrm{~V}$ sources by short circuits, leaving the $57.0 \mathrm{~V}$ source intact. (d) Repeat part (b) by replacing the $92.0 \mathrm{~V}$ and $57.0 \mathrm{~V}$ sources by short circuits, leaving the $55.0 \mathrm{~V}$ 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). (f) If the $57.0 \mathrm{~V}$ source is replaced by an $80.0 \mathrm{~V}$ source, what will be the new currents in all branches of the circuit?
( FIGURE CAN'T COPY )