Question 6: Current Electricity

Question

A metal wire has a resistance of $$35 \Omega$$. If its length is increased to double by drawing it, then its new resistance will be

Accepted Answer

Given, $$R_1=35 \Omega, l_2=2 l_1$$
On increasing the length,
$$\begin{aligned}
m_1 & =m_2 \
	herefore \quad ho A_1 l_1 & =ho A_2 l_2 \
\pi r_1^2 l_1 & =\pi r_2^2 l_2 \
\frac{r_1^2}{r_2^2} & =\frac{l_2}{l_1} \
\frac{r_1^2}{r_2^2} & =\frac{2 l_1}{l_1} \
\frac{r_1^2}{r_2^2} & =2 \quad 	ext{..... (i)}\
\frac{R_1}{R_2} & =\frac{ho \cdot \frac{l_1}{\pi r_1^2}}{ho \cdot \frac{l_2}{\pi r_2^2}} \
& =\frac{l_1}{l_2} \cdot \frac{r_2^2}{r_1^2}=\frac{l_1}{2 l_1} \cdot \frac{1}{2} \
\frac{R_1}{R_2} & =\frac{1}{4} \
& R_2=4 R_1=4 	imes 35=140 \Omega
\end{aligned}$$

Answer

$$70 \Omega$$

Answer

$$140 \Omega$$

Answer

$$105 \Omega$$

Answer

$$35 \Omega$$

Current Electricity

A metal wire has a resistance of $35 \Omega$. If its length is increased to double by drawing it, then its new resistance will be

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