Question

2. A circuit is constructed with three 5 W resistors. What is the maximum and minimum current drawn from a 12 V battery with some combination of all three of these resistors? Is there a third level of current possible?

Answer 1

First, find the resistance of the resistors keeping in mind that power is voltage squared divided by resistance:

$$P=\frac{V^2}{R}\rightarrow R=\frac{V^2 }{P}=\frac{12^2}{5}=28.8\space\Omega.$$

Three resistors in parallel produce the highest resistance and lowest current:

$$R_0=3R=86.4\space\Omega,\\\space\\ I_L=\frac{V}{R_0}=\frac{12}{86.4}=0.14\text{ A}.$$

Three resistors in parallel produce the smallest resistance and highest current:

$$R_0=\frac{R}{3}=9.6\space\Omega,\\\space\\ I_H=\frac{V}{R_0}=\frac{12}{9.6}=1.25\text{ A}.$$

If we connect two resistors in parallel and then connect a third resistor to their common node, the resistance will be

$$R_0=\frac{R}{2}+R=1.5R=43.2\space\Omega,\\ I_M=\frac{V}{R_0}=\frac{12}{43.2}=0.28\text{ A}.$$