Question about resistors

[virtuoso735]

I am confused about a question in BR Physics Book 2 Section IX (Electricity and Electric Currents). It's in Passage I in the 25-question review section (p. 202). The question is as follows:

3. In a Joule heating experiment, which of the following changes would increase the rate at which the solution temperature rises?

I. Decreasing the mass of the solution.
II. Increasing the specific heat of the solution.
III. Increasing the voltage of the battery.
IV. Increasing the resistance of the resistor.

The answer is I and III only, but I don't understand why increasing the resistance wouldn't increase the rate of temperature increase. Figure 2 seems to show that the resistor with lower resistance has a larger temperature increase, but why is that?

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[MT Headed]

The rate at which energy is delivered is called power. In electrics, P=IV (and as always V=IR). So P=(I^2)R, which is great if you have a known constant current, or P=(V^2)/R, which is great if you have a known constant voltage. In your case, the voltage is a constant, so as R goes up, P goes down.

On a more intuitive level, to deliver power you gotta move some electrons, and if you increase the resistance you ain't moving them much. Also, think about the extreme cases: at infinite resistance you have cut the wires and nothing will happen; at zero resistance, you have a short circuit and the whole contraption will probably catch on fire.

 

[drechie]

the passage says:
if two resistors experience the same current, then the one with greatest resistance dissipates the most heat


i figured the greater the resistance, the larger the heat, the more quickly the water will heat up. what did i do wrong?

 

[Cawolf]

if two resistors experience the same current, then the one with greatest resistance dissipates the most heat

That answer choice indicates that the current is a variable and the voltage is constant. Read the post above yours for a good explanation as to why power is inversely proportional to resistance when voltage is constant.

Therefore increasing the resistance will decrease the power - decreasing the rate that the solution heats up.