I have a question about resistors...Wouldn't a 40-ohm resistor be the hottest while the 20-ohm resistor is the coolest or is it the other way around?
If the voltage across the circuit is 120 V and has a 12-A fuse, will the fuse melt if all the lamps and the heater are on?
The fuse will melt if the sum of all component currents > 12 A. Refer to your other question to see if that is the case.
To determine which resistor would be the hottest and which one would be the coolest, we need to consider the concept of power dissipation in resistors. Power dissipation in a resistor is given by the formula P = I^2R, where P is the power in watts, I is the current in amperes, and R is the resistance in ohms.
Looking at the equation, we can see that the power dissipation is directly proportional to the current and the resistance. Therefore, the resistor that dissipates more power will be hotter.
In this case, if we assume that both resistors have the same current passing through them, the 40-ohm resistor will have higher power dissipation than the 20-ohm resistor. This is because with the same current, a higher resistance will result in more power being dissipated. So, the 40-ohm resistor will be the hotter one, while the 20-ohm resistor will be cooler.
Regarding the second question about the fuse melting, we need to determine whether the total current drawn by the lamps and the heater exceeds the rated current of the 12-A fuse.
If we know the power ratings of the lamps and the heater, we can calculate the total power by adding up the power consumed by each device. Then, using the formula P = IV, where P is the power in watts, I is the current in amperes, and V is the voltage in volts, we can determine the total current draw.
If the total current drawn by all the devices is less than or equal to 12 A, the fuse should not melt. However, if the total current exceeds 12 A, the fuse will likely melt and interrupt the circuit to prevent damage or a potential fire hazard.
To sum up, the 40-ohm resistor would be hotter than the 20-ohm resistor, while the fuse will melt if the total current drawn by the lamps and the heater exceeds the rated current of the fuse.