Question

explain why both voltage and current for a resistor dont need to br continuous in time. why can it "jump"?

Answer 1

Resistance is the property of a conductor due to which it oppose the flow of current. This resistance is does not depend upon the nature of the current and the voltage.

This resistance is given by the relation

this R depend on length(l), relaxation time(tau),area(A) and number of free electron(n) of conductor.

And according to ohms law

and

R is constant of the proportionality.

if we applied a sinusoidal voltage than we get the sinusoidal  current acroos the resistance and if we apllied the constant voltage across the resistor then we get constant current.