Let's first find the total resistance of three resistances connected in parallel:
Rtot1=R11+R21+R31,Rtot=R11+R21+R311,Rtot=12 Ω1+16 Ω1+20 Ω11=5 Ω.Finally, we can find the resistance that must be connected in series with this combination to give a total resistance of 25 ohms:
Rtot,parallel+R=Rtot,series,R=Rtot,series−Rtot,parallel=25 Ω−5 Ω=20 Ω.Answer:
R=20 Ω.
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