Answer:
1.25 A
Step-by-step explanation:
The superposition theorem tells you the behavior of the circuit can be found by summing the behaviors resulting from considering one source at a time.
Application
For the purpose of analysis using the superposition theorem, each voltage source not being analyzed is replaced by a short circuit. When we do that for either of the top two sources, the result is the equivalent circuit shown in the attachment.
The equivalent circuit shown can be further simplified for analysis purposes. The resistor on the left can be ignored, as its value has no effect on the current in the 20Ω resistor.
The voltage source and the two 8Ω resistors on the right can be replaced by their Thévenin's equivalent: V/2 in series with 4Ω. After this transformation, the circuit is a series circuit, and the current in the 20Ω resistor is the current from a source of V/2 through a total resistance of (4+20)Ω. That is ...
I = V/R = (V/2)/((4+20)Ω) = V/48 amperes
For the bottom voltage source, replacing the other two sources by zero ohms effectively shorts out the entire part of the circuit containing the 20Ω resistor. Hence the contribution to the current from the 30V source is zero.
The sum of the currents from the two top voltage sources is then ...
20/48 +40/48 = 60/48 = 5/4 . . . amperes
The current flowing in the 20Ω resistor is 1.25 amperes.
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Additional comment
Using Thévenin's equivalents can often simplify analysis dramatically, even to the point where it can be accomplished mentally.
This result was verified by analyzing the circuit using mesh currents.