Question

a wire of resistance R is cut into 3 equal parts
a)find the new resistance in terms of original resistance "R"
B)if these three pieces are connected in parallel what is the ratio of equivalent resistance so obtained with original resistance.

Answer 1

a. wire of resistance R is cut into three equal parts means resistance of 3 wires = R
then resistance of 1 wire = R/3
so, the new resistance will be R/3
b. if these wires are connected in parallel then equivalent resistance will be :
1/R = 3/R + 3/R + 3/R
= 3+3+3/R
=9/R, 1/R=9/R
R=R/9
so R is

so, R/9 is the equivalent resistance of three wires.
and the original resistance is R
so, the ratio of equivalent resistance and original resistance is = R/9/R = R/9R = 1/9
= 1:9