The equivalent resistance of three resistors A, B and C connected in parallel is 1Ω.?
If A is twice of B and C is half as much as B, find the equivalent resistance when the three of them are connected in series.
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Let R be the resistance of B
Then,
A=2R
C=R/2
When the three resistances are connected in parallel,
1/Req = 1/A + 1/B + 1/C
1/Req = 1/2R + 1/R + 2/R
= 1/2R + 2/2R + 4/2R
= 7/2R
Req = 2R/7 = 1Ω
R = 7/2 Ω
Thus A= 7Ω, B=7/2 Ω C=7/4Ω
The equivalent resistance when A, B, C are in series:
Rseries = A + B + C
= 7 + 7/2 + 7/4
= 49/4 Ω
= 12.25 Ω