Question 198: Current Electricity

Question

A $$1 \mathrm{~m}$$ long wire is broken into two unequal parts $$\mathrm{X}$$ and $$\mathrm{Y}$$. The $$\mathrm{X}$$ part of the wire is streched into another wire W. Length of $$W$$ is twice the length of $$X$$ and the resistance of $$\mathrm{W}$$ is twice that of $$\mathrm{Y}$$. Find the ratio of length of $$\mathrm{X}$$ and $$\mathrm{Y}$$.

Accepted Answer

$$
\frac{\mathrm{R}_{\mathrm{X}}}{\mathrm{R}_{\mathrm{Y}}}=\frac{\ell_{\mathrm{X}}}{\ell_{\mathrm{Y}}}
$$
When wire is stretched to double of its length, then resistance becomes 4 times
$$
\begin{aligned}
&\mathrm{R}_{\mathrm{W}}=4 \mathrm{R}_{\mathrm{X}}=2 \mathrm{R}_{\mathrm{Y}} \\
&\frac{\mathrm{R}_{\mathrm{X}}}{\mathrm{R}_{\mathrm{Y}}}=\frac{1}{2}
\end{aligned}
$$
So. $\frac{\ell_{\mathrm{x}}}{\ell_{\mathrm{y}}}=\frac{1}{2}$

Answer

1 : 4

Answer

1 : 2

Answer

4 : 1

Answer

2 : 1

Current Electricity

Choose the correct answer: