Question

**OR** **(b)** How would you join three resistors each of resistance $6\ \Omega$, so that the equivalent resistance of the combination is (i) $9\ \Omega$, and (ii) $4\ \Omega$?

Accepted Answer

(i) **To get $9\ \Omega$:** Connect two $6\ \Omega$ resistors in parallel and connect this combination in series with the third $6\ \Omega$ resistor. $$R_{eq} = (6 \parallel 6) + 6 = 3 + 6 = 9\ \Omega$$ (ii) **To get $4\ \Omega$:** Connect two $6\ \Omega$ resistors in series and connect this combination in parallel with the third $6\ \Omega$ resistor. $$R_{eq} = (6 + 6) \parallel 6 = 12 \parallel 6 = \frac{12 	imes 6}{12 + 6} = \frac{72}{18} = 4\ \Omega$$

Combination of three 6-ohm resistors

Explanation

Practise this under board exam conditions