[Physics] Relationship among heat generated, power, current and voltage

electric-currenthomework-and-exercisespowervoltage

Can you help me understand the relationship between current, voltage and heat generated?

I tried two sets of heated gloves. One uses a battery which generates 7.4 volts x 2 amperes (14.8 watts of power). The other uses an 11.1 volt x 1.4 ampere battery (15.54 watts of power). So, the power generated is similar, but the 11.1 volt gloves heat my hands much more. Why is that?

My memories of high school physics are distant, but I remember one can think of electricity in analogy with a water system, whereby volts are the water pressure, current (measured in amperes) is the flow of water, resistance is the size of the pipe, and power (watts) = volts x current.
I also remember the amount of heat generated is proportional to the square of the current, but I’m not sure how to put all the pieces together and explain why the 11.1 volt gloves generate much more heat.

Best Answer

More the power, more the heat generated.

$$P(\textrm{Power})=V\cdot I$$ $$H(\textrm{in joules})\propto V\cdot I\cdot t\,(\textrm{in s})$$ $$ \therefore H(\textrm{in joules})\propto P\cdot t (\textrm{in s})$$

The 11.1 volt gloves does not give greater heat just because it has more Potential difference, but because $\textrm{Power}$ is greater in it.