Question

21. A meter bridge is used to determine the resistance of an unknown wire by measuring the balance point length l. If the wire is replaced by another wire of same material but with double the length and half the thickness , the balancing point become 2l, then the value of l is
(a) 40 cm
(b) 20 cm
(c) 300/7 cm
(d) 240/7 cm

Answer 1

$$\begin{gathered} Letresis\tan ceoffirstwirebe{R}_{1}andthatofsecondbe{R}_2 \\ {R}_1=\rho \frac{l}{A}=R_1=\rho \frac{l}{A}=\rho \frac{l}{\pi r^2} \\ Acordingtoquestion \\ {R}_2=\rho \frac{2l}{\pi {\left({\displaystyle \frac{r}{2}}\right)}^2}=8\rho \frac{l}{\pi r^2}=8R_1 \\ \frac{R_1}{R_2}=\frac{1}{8} \\ Weknowthat,inamaterbridge \\ R=\frac{l}{100-l}X,whereXistheknownresi\tan ceconnectedtotheotherarmofmeterbridge \\ Let \\ {R}_1=\frac{l}{100-l}X \\ then \\ {R}_2=\frac{2l}{100-2l}X \\ \frac{R_1}{R_2}=\frac{\frac{l}{100-l}X}{\frac{2l}{100-2l}X} \\ \frac{1}{8}=\frac{\frac{1}{100-l}}{\frac{2}{100-2l}}=\frac{1}{2}\times \frac{100-2l}{100-l} \\ \frac{1}{4}=\frac{100-2l}{100-l} \\ 100-l=400-8l \\ 7l=300 \\ l=\frac{300}{7}cm \end{gathered}$$