Question

A simple way to heat water (or better yet, hot chocolate) in your car is to use a small immersion heater. This is nothing more than a simple resistor that is waterproof so you can dunk it in your beverage. The resistor is connected to the car's 12-V battery and, through electrons colliding with the lattice as discussed in class, the resistor heats up and gives the heat to your beverage.
a) If the resistance of the heater was increased, would it speed up or slow down the heating process? Explain your answer.

b) Immediately after turning on the heater, is the current in the circuit increasing, decreasing, or remaining constant? Assume the resistor is made of Nichrome wire. Explain your answer.

Answer 1

Answer:

a) Slow down

b) Decreasing.

Explanation:

a) The energy that is converted to heat can be written as:

$P=V^2/R$

As the resistance increases, with constant voltage, the amount of power dissipated as heat decreases (less current trought the resistor).

Then, we can conclude that, as the energy dissipated by the resistor is less as its resistance is increased, the heating process will slow down.

b) We have to evaluate what happens with the resistivity of the resistor during the heating.

We know that resistivity of a nichrome wire increases with the temperature. With the conclusion of the previous question, if the resistivity increases and the voltage stays constant, the current in the circuit will decrease as the resistor became hotter.

We can conclude this using the Ohm's law:

$I=V/R$