Question

By what factor does the resistance of a copper wire change if its length quadruples and its diameter quadruples? (If the resistance doubles, enter "2"; if it decreases by a factor of three, enter "1/3", etc.)

(4/9 is not correct)

Answer 1

as we know that the resistance of coppor wire

R = ( rho x L ) A

here A = pie x r²

where r is the radious of coppor wire

r = d / 2

so the resistance

R = ( rho x L ) / ( pie xd² / 4 )

so the resistance is depend on the length and diometer of the wire

if the length of wire increse the diometer of wire is also increse

so the resistance will remains constant

similarly if the diometer of the wire increses naturally the length of wire will also increses

so the resistance will remains constant

so the resistance will not change