What possible values of resultant resistance one can get by combining two resistances, one of value 2 ohm and the other 6 ohm?

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Solution

Case 1
Connecting a 2 Ω and 6 Ω resistor in series combination:
R = R₁ + R₂
R =2 $Ω$ + 6 $Ω$ =8 $Ω$
Thus, we will get an 8 Ω resistor.

Case 2
Connecting a 2 Ω and 6 Ω resistor in parallel combination:

$\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \frac{1}{R} = \frac{1}{2} + \frac{1}{6} \Rightarrow \frac{1}{R} = \frac{4}{6} \Rightarrow R = \frac{6}{4} Ω$
Thus, we will get a 1.5 Ω resistor.

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What possible values of resultant resistance one can get by combining two resistances, one of value 2 ohm and the other 6 ohm?

Case 1 Connecting a 2 Ω and 6 Ω resistor in series combination: R = R1 + R2 R =2 Ω + 6 Ω =8 Ω Thus, we will get an 8 Ω resistor. Case 2 Connecting a 2 Ω and 6 Ω resistor in parallel combination: 1R=1R1+1R21R=12+16 ⇒1R=46⇒R=64 Ω Thus, we will get a 1.5 Ω resistor.