How can three resistors of resistances 2 ?, 3 ?, and 6 ? be connected to give a total resistance of (a) 4 ?, (b) 1 ??

Answers (1)

(a) R_1=3,R_2=6,R_3=2

    R=Equivalent  resistance

    frac1R_1_2=frac1R_1+frac1R_2 

Rightarrow frac1R_1_2=frac13+frac16

Rightarrow frac1R_1_2=frac2+16

Rightarrow R_1_2=frac63=2

R=R_1_2+R_3=2+2=4

(b).1 Ohm

  R=Equivalent  resistance

Connect all the three resistors in parallel

    frac1R=frac1R_1+frac1R_2+frac1R_3 

Rightarrow frac1R=frac12+frac13+frac16

Rightarrow frac1R=frac6+3+16

Rightarrow R=frac166=1Omega

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