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Q.11. Show how you would connect three resistors, each of resistance $6\Omega$ , so that the combination has a resistance of (i) $9\Omega$ , (ii) $4\Omega$ .

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(i) $R_1=R_2=R_3=6$

R=Equivalent resistance

$\frac{1}{R_1_2}=\frac{1}{R_1}+\frac{1}{R_2}$

$\Rightarrow \frac{1}{R_1_2}=\frac{1}{6}+\frac{1}{6}$

$\Rightarrow \frac{1}{R_1_2}=\frac{1+1}{6}$

$\Rightarrow R_1_2=\frac{6}{2}=3$

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

(ii)

. $R_1=R_2=R_3=6$

R=Equivalent resistance

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

$\frac{1}{R}=\frac{1}{R_1_2}+\frac{1}{R_3}$

$\Rightarrow \frac{1}{R}=\frac{1}{12}+\frac{1}{6}$

$\Rightarrow \frac{1}{R}=\frac{1+2}{12}$

$\Rightarrow R=\frac{12}{3}=4$

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