Question

Show how you would connect three resistors, each of resistance $6\Omega$, so that the
combination has a resistance of (i) $9\Omega$ (ii) $2\Omega$

Answer 1

(i) In order to get a resistance of $9\Omega$ from three resistors, each of resistance $6\Omega$, we connect two resistors in parallel and this parallel combination (or resistance $3\Omega$) in series with the third resistor as shown in fig.

(ii) In order to get a resistance of $2\Omega$ from three resistors, each of resistance $6\Omega$, we connect all the three resistors in parallel as shown in fig (b) as equivalent resistance in parallel combination, i.e., $R_p$ is given by $R_p=\frac{6\Omega }{3}=2\Omega$