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How can three resistors of resistances 2 Ω, 3 Ω and 6 Ω be connected to give a total resistance of (a) 4 Ω, (b) 1 Ω
(a) To get 4 Ω equivalent resistance, 3 Ω and 6 Ω resistors are connected in parallel and 2 Ω in series.
When 3 Ω and 6 Ω are added in parallel.
1/RP = 1/R1 + 1/R2
1/RP = 1/3 + 1/6
1/RP = (2+1)/6
1/RP = 3/6
= 2Ω
When its equivalent resistance is connected in series with a resistor of 2 Ω, then
RS = R1 + R2
RS = 2 + 2
= 4Ω
When all three resistors are connected, the equivalent resistance is 1 Ω.
1/RP = 1/R1 + 1/R2 + 1/R3
1/RP = (3 +2 + 1)/6
1/RP = 6/6
= 1/1
RP = 1Ω
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