How can 3 resistors of resistances of 2 ohm, 6 ohm, 3 ohm be connected to give a total resistance of (a) 4 ohm (b) 6.1 ohm

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Asked: 2023-05-27T03:48:41+05:30 In: Science
How can 3 resistors of resistances of 2 ohm, 6 ohm, 3 ohm be connected to give a total resistance of (a) 4 ohm (b) 6.1 ohm

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  2. Gandalf
    Step1:Combination to get 4 ohm equivalent resistance
     
    Three resistors of resistances 2ohm,3ohm, and 6ohm respectively.
     Let R1​=2Ω⇒R2​=3Ω⇒R2​=6Ω​
     
    To obtain a total resistance of 4Ω from three resistors of given resistances, Firstly, connect the two resistors of 3Ω and 6Ω in parallel to get a total resistance of 2Ω which is less than the lowest individual resistance.
    When R2​ and R3​ are connected in parallel with R1​ in series we get
    ⇒1/R=1/R2​+1/R3​⇒1/R=1/3+1/6⇒1/R=1/2⇒R=2Ω⇒ Resistance in series =R+R1​=2+2=4Ω​
    Hence, the total resistance of the circuit is 4Ω.
    Step2:Combination to get 1 ohm equivalent resistance
     
    To get a total resistance of 1Ω from three resistors of 2Ω,3Ω and 6Ω, all the three resistors should be connected in parallel.
    When R1​,R2​,R2​ are connected in parallel we get
    ⇒1/R=1/R1​+1/R2​+1/R3​⇒1/R=1/2+1/3+1/6⇒1/R=1Ω​
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