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

(i) We can get a total resistance of 4$$\Omega$$ by connecting the 2$$\Omega$$ resistance in series with the parallel combination of 3$$\Omega$$ and 6$$\Omega$$.
So, $$R=R_1+\frac{R_2R_3}{R_2+R_3}= 2+\frac{6×3}{6+3}=4\Omega$$

(ii) We can obtain a total resistance of 1$$\Omega$$ by connecting resistors of 2$$\Omega$$, 3$$\Omega$$ and 6$$\Omega$$ in parallel.

$$\frac{1}R=\frac{1}{R_1} +\frac{1}{R_2}+\frac{1}{R_3}=\frac{1}{2} +\frac{1}{3}+\frac{1}{6}$$

$$\frac{1}R=1 \Omega$$

or R=1 $$\Omega$$