Question

When the diameter of a wire is doubled, its resistance becomes
(a) double
(b) four times
(c) one-half
(d) one-fourth

Answer 1

Answer:

4 times

Explanation:

doubled means twice and it becomes four times that of D ,i.e 2d=4R

Answer 2

Resistance Becomes One Fourth  

Explanation:

• Factors upon which Resistance depends are -

Resistivity, Length and Area of Cross-section  

which have been associated in the below relation -

$Resistance = Resistivity \times \frac {Length}{Area\ of\ Cross-section}$

= $Resistivity \times \frac {Length}{\pi r^2}$

1.) Resistivity - depends upon wire material (if material does not change then resistivity also)

2.) Length of wire remains same (No change is given)

3.) And Area is inversely proportional to $\pi \times square\ of\ radius$

Hence,  

Radius is Two Times, which means  

Resistance = $\frac {1}{r^2}$

= $\frac {1}{2^2}$

= $\frac {1}{4}$