#### (Solved): I Recently Stated Several Relations In Lecture Without Providing Any Proof. You Will Work Out The De ...

I recently stated several relations in lecture without providing any proof. You will work out the derivations in this homework. We will use only Ohmâ€™s law, the junction rule, and the ideas from previous chapters such as electric potential, work, energy, etc.

Problem 1: The first task is to prove the relation I gave in lecture for the power dissipated by a resistor. Consider a single resistor with a known value of R connected to a battery of voltage V , as in Fig. 1

i ) Given that we know the resistance and the voltage, we can find the current using Ohmâ€™s law. How much charge flows through the resistor is a short amount of time dt? You may write this either in terms of R and V or by using the current I.

ii ) Every charge that goes through the resistor must go through a potential difference of magnitude V . Given this idea, how much total energy is lost by the charge carriers in a time dt?

iii ) The total energy lost, divided by the time it took gives the power. So for this last step, simply divide your result from ii by d t to get the power dissipated by the resistor. For completeness, use Ohmâ€™s law to write the power in three ways, one without R, one without V and finally one without I.

Figure 1: