CBSE BoardEnglish MediumSTD 10ScienceElectricity1 Mark
MCQ
When the diameter of a wire is doubled, its resistance becomes :
A
Double.
B
Four times.
C
One $-$ half.
✓
One $-$ fourth.
✓
Answer
Correct option: D.
One $-$ fourth.
$\text{R}=\rho\frac{\text{I}}{\text{A}}$
When the diameter is doubled $, d = 2d$
Radius $, r\ ' = 2r$
Area of cross section, $\text{A}'=\pi\text{r}'^2=\pi(2\text{r})=4\pi\text{r}^2=4\text{A}$
The area of cross-section will increase by four times.
Then the new resistance, $\text{R}'=\frac{\rho\text{I}}{\text{A}'}$
$\text{R}'=\frac{\rho\text{I}}{4\text{A}}$
$\text{R}'=\frac{\text{R}}{4}$
Thus, the resistance will get reduced by four times.
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