Show how you would connect there resistors each of resistance 6 so that the combination of a resistance of (1)9 (2)4
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Answer:
(1) 2 in parallel and one in series with the parallel combination
(2) 2 in series and one in parallel with the series combination
Explanation:
To know :
- When resistors of resistances R₁ , R₂ , R₃ .... are connected in series, the equivalent resistance is given by
R = R₁ + R₂ + R₃ + ...
- When resistors of resistances R₁ , R₂ , R₃ .... are connected in parallel, the equivalent resistance is given by
1/R = 1/R₁ + 1/R₂ + 1/R₃ + ...
Solution :
Given : resistance of each resistor = 6Ω
1. To get the combined resistance of 9Ω,
The two resistors should be connected in parallel and the third resistor in series with this parallel combination.
- when two resistors are connected in parallel, equivalent resistance,
1/Rₚ = 1/6 + 1/6
1/Rₚ = 2/6 = 1/3
Rₚ = 3Ω
- when the third resistor is connected in series with this parallel combination, equivalent resistance
R = 3Ω + 6Ω = 9Ω
2. To get the combined resistance of 4Ω,
The two resistors should be connected in series and the third resistor in parallel with this series combination.
- when the two resistors are connected in series, equivalent resistance
Rₛ = 6Ω + 6Ω = 12Ω
- when the third resistor is connected in parallel with this series combination, equivalent resistance
1/R = 1/6 + 1/12
1/R = (2+1)/12
1/R = 3/12 = 1/4
R = 4Ω
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