Question

A metallic conductor at 10${}^o$C connected in the left gap of Meter Bridge gives balancing length 40 cm. When the conductor is at 60${}^o$C, the balance point shifts by 5 cm. The temperature coefficient of resistance of the material of the wire

• A. (1 / 210) /${}^o$C
• B. (1 / 220) /${}^o$C
• C. (1 / 200) /${}^o$C
• D. (1 / 201) /${}^o$C

Answer 1

Answer: (B)

(1 / 220) /${}^o$C

$R_1-InitialR\left({10}^{0}C\right)$

$R_2-FinalR\left({20}^{0}C\right)$

$\frac{R_1}{Q}=\frac{40}{60}=\frac{2}{3}$

$\frac{R_2}{Q}=\frac{45}{55}$

$\frac{R_1}{R_2}=\frac{2\times 11}{3\times 9}$

$\frac{R_1}{R_2}=\frac{22}{27}$

$\frac{1}{1+\alpha \Delta T}=\frac{22}{27}\Rightarrow \frac{22}{27}=1+\alpha \Delta T$

$\Rightarrow \frac{5}{22\times 50}=\alpha \Rightarrow \alpha =\frac{1}{220}$