Answer to Question #155914 in Electric Circuits for Jerick

Question #155914

Three resistances of 12, 16, and 20 ohms are connected in parallel. What resistance must be connected in series with this combination to give a total resistance of 25 ohms?


1
Expert's answer
2021-01-15T13:46:49-0500

Let's first find the total resistance of three resistances connected in parallel:


1Rtot=1R1+1R2+1R3,\dfrac{1}{R_{tot}}=\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}+\dfrac{1}{R_{3}},Rtot=11R1+1R2+1R3,R_{tot}=\dfrac{1}{\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}+\dfrac{1}{R_{3}}},Rtot=1112 Ω+116 Ω+120 Ω=5 Ω.R_{tot}=\dfrac{1}{\dfrac{1}{12\ \Omega}+\dfrac{1}{16\ \Omega}+\dfrac{1}{20\ \Omega}}=5\ \Omega.

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_{tot,parallel}+R=R_{tot,series},R=Rtot,seriesRtot,parallel=25 Ω5 Ω=20 Ω.R=R_{tot,series}-R_{tot,parallel}=25\ \Omega-5\ \Omega=20\ \Omega.

Answer:

R=20 Ω.R=20\ \Omega.


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