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Q.

A potentiomete wire of 10m length and 20 Ohm resistance is connected in series with a resistance R ohms and a battery of emf 2V, negligible internal resistance. Potential gradient on the wire is 0.16 millivolt/centimetre then R is____ ohms

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a

60

b

50

c

230

d

46.6

answer is C.

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Detailed Solution

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$\begin{array}{l} \frac{V}{ℓ} = \frac{{ER}_{w}}{(r + R_{s} + R_{w}) L} = \frac{2 \times 20}{(0 + R + 20) \times 10} = 16 \times 10^{- 5} \times 10^{2}; \\ \Rightarrow \frac{40}{10 (R + 20)} = 16 \times 10^{- 3}; \\ \Rightarrow \frac{4}{1000} = \frac{1}{R + 20}; \\ ∴ R = 230 Ω \end{array}$

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