Five resistors are connected in a circuit as shown. Assume the battery has negligible internal resistance.
What is the equivalent resistance of this set of resistors?
3 ohms. The top part of the circuit has 4 and 12 in parallel, which is 3, in series with another 3 which makes 6 ohms. The 9 and 18 in parallel in the bottom part also make 6 ohms. 6 and 6 in parallel gives 3 ohms.
Comparing just the 3 W, 9 W, and 12 W resistors, rank them according to the current passing through them.
In terms of current we have 3 W > 9 W > 12 W. Because the top and bottom branches of the circuit have the same resistance the current I splits equally between them. The 3 W resistor gets I/2, while the 9 W resistor gets (2/3) I/2 = I/3. The 12 W resistor gets (1/4) I/2 = I/8.
Rank the same three resistors based on the potential difference across them.
9 W > 3 W = 12 W. The 9 W resistor has the full battery voltage, 10 V across it. The other two have 5 V each because the 4 and 12 in parallel are equivalent to a 3 W resistor.