Question $1(8$ pts$)$ We must constantly be aware of the limitations of superposition. It is

applicable only to linear responses. The most common nonlinear response is power.

a$)$ For a resistor, what is the relation of power with voltage only?

b$)$ For a resistor, what is the relation of power with current only?

c$)$ Why is power a non$-$linear response?

d$)$ Consider two $1$ V batteries in series with $1$ resistor. Use this circuit to prove that

superposition cannot be used to calculate non$-$linear responses, like power