Question

a potential difference V is applied across a conductor of length L and diameter D. How are the electric field E and the resistance R of the conductor affected when in turn
a) V is halved
b) L is halved
c) D is doubled
Justify and assume in each case, other factors are constant

Answer 1

$$\begin{gathered} Electricfieldacrosstheconductorisgivenby; \\ E=\frac{V}{L} \\ andresisatnceisgivenby" \\ R=\frac{\rho L}{\pi \left({\displaystyle \frac{D^2}{4}}\right)} \\ \left(1\right)WhenVishalved,thenEbecomehalf. \\ \left(2\right)whenLishalved,EbecomesdoubleabdRbecomeshalf \\ \left(3\right)Disdoubled,rbecomes1/4oftheinitialvalue. \end{gathered}$$