Answer
See answers.
Work Step by Step
There are at least 2 methods. The first method is to connect resistors in series. We’re told that each resistor can dissipate 0.5 W. For the combination to dissipate 3.5W, we need 7 resistors. The equivalent resistance of $3.2 k\Omega$ is the sum of the resistances, because they are in series.
$$R_{eq}=3200\Omega=7R$$
$$R=457\Omega$$
Connect 7 such resistors in series to form a $3.2 k\Omega$ resistor that can handle 3.5 watts.
An alternate method is to connect resistors in parallel. We’re told that each resistor can dissipate 0.5 W. For the combination to dissipate 3.5W, we again need 7 resistors. The equivalent resistance of $3.2 k\Omega$ is 1/7 the resistance of an individual resistor, because they are in parallel.
$$R_{eq}=3200\Omega=\frac{1}{7}R$$
$$R=22.4k\Omega$$
Connect 7 such resistors in parallel to form a $3.2 k\Omega$ resistor that can handle 3.5 watts.
