(A) Show how you would connect three resistors each of resistance $6\Omega$, so that the combination has a resistance of $9\Omega$. Also justify your answer. OR (B) In the given circuit calculate the power consumed in watts in the resistor of $2\Omega$ :

To connect three resistors each of resistance $6\Omega$ so that the combination has a resistance of $9\Omega$, we can connect them in parallel. This is because when resistors are connected in parallel, the total resistance is less than any of the individual resistances. The formula for the total resistance of resistors connected in parallel is: rac{1}{R_{total}} = rac{1}{R_1} + rac{1}{R_2} + rac{1}{R_3} where $R_{total}$ is the total resistance and $R_1$, $R_2$, and $R_3$ are the individual resistances. In this case, we have: rac{1}{R_{total}} = rac{1}{6} + rac{1}{6} + rac{1}{6} = rac{3}{6} = rac{1}{2} Therefore, the total resistance is $2\Omega$. However, we want the total resistance to be $9\Omega$, so we need to adjust the connection. One way to do this is to connect two of the resistors in series and then connect the third resistor in parallel with the series combination. The formula for the total resistance of resistors connected in series is: $$R_{total} = R_1 + R_2 + R_3$$ In this case, we have: $$R_{total} = 6 + 6 = 12\Omega$$ Now, we can connect the third resistor in parallel with the series combination: rac{1}{R_{total}} = rac{1}{12} + rac{1}{6} = rac{3}{12} = rac{1}{4} Therefore, the total resistance is $4\Omega$. However, we still need to adjust the connection to get a total resistance of $9\Omega$. One way to do this is to add another resistor in series with the parallel combination. Let's call this resistor $R_4$. The formula for the total resistance of resistors connected in series is: $$R_{total} = R_1 + R_2 + R_3 + R_4$$ In this case, we have: $$R_{total} = 4 + R_4$$ We want the total resistance to be $9\Omega$, so we can set up the equation: $$4 + R_4 = 9$$ Solving for $R_4$, we get: $$R_4 = 5\Omega$$ Therefore, we need to add a resistor of $5\Omega$ in series with the parallel combination to get a total resistance of $9\Omega$.