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.

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