Show how you would connect three resistors, each of resistance 6 ?, so that the combination has a resistance of (i) 9 ?, (ii) 4 ?.

Answers (1)

(i) R_1=R_2=R_3=6

    R=Equivalent  resistance

    frac1R_1_2=frac1R_1+frac1R_2 

Rightarrow frac1R_1_2=frac16+frac16

Rightarrow frac1R_1_2=frac1+16

Rightarrow R_1_2=frac62=3

R=R_1_2+R_3=3+6=9Omega

(ii)

.R_1=R_2=R_3=6

  R=Equivalent  resistance

R_1_2=R_1+R_2=6+6=12Omega

 

  frac1R=frac1R_1_2+frac1R_3 

Rightarrow frac1R=frac112+frac16

Rightarrow frac1R=frac1+212

Rightarrow R=frac123=4

 

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