Question 1
Applying the superposition theorem to the circuit shown, the voltage across resistor R2 would be:
![](data:image/png;base64, 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)
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5 V.
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10 V.
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15 V.
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8 V.
Question 2
Applying the superposition theorem to the circuit shown, the voltage across resistor R1 would be:
![](data:image/png;base64, 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