A potential difference V is applied across a conductor of length L and diameter D. how the electric field E and resistance R affected when:
(1) V is halved (2) L is halved (3) D is doubled
justify answer in each case
Electric field E = potential difference / length of conductor
Electric field is directly proportional to voltage applied and inverself proportional to length of conductor.
and resistance = (resistivity x length of conductor) / area of cross section
resistance is directly proportional to length and inversely to the area of cross section.
you can write area of cross section as pi(D square) /4
(1) V is halved.
E = V/L
E gets half
On halving voltage, current will also get half by Ohm's law V = IR. such that R will remain unchanged.
(2) L is halved
E will double.
Resistance will become half
(3) D is doubled
E is independent of area of cross section. so it will remain unchaged.
Resistance depends inversely with area. If D is doubled Area will become 4 times, and therefore R will become 1/4 times the orginal.