Question 23: Current Electricity

Question

A potentiometer wire, 10 m long, has a resistance of 40$\Omega$. It is connected in series with a resistance box and a 4 V storage cell. If the potential gradient along the wire is 0.4 mV cm
$-$1
, the resistance unplugged in the box is

Accepted Answer

Given, potential gradient = 0.4 mV cm
$-$1
= 0.4 $	imes$ 10
$-$3
V cm
$-$1
Length of wire, l = 10 m = 1000 cm
Electromagnetic force of cell, E = 4 V
Potential gradient along wire = ${{potential\,difference\,along\,wire} \over {length\,of\,wire}}$
$ \Rightarrow 0.4 	imes {10^{ - 3}} = {{l 	imes 40} \over {1000}}$ V cm
$-$1
Let R be the required resistance unplugged in the box.
$	herefore$ Current in wire, $l = {4 \over {400}}A$ ...... (i)
Also, $l = {E \over {R + R'}} = {4 \over {40 + R}}$ ....... (ii)
Equating Eq. (i) and (ii), we get
${4 \over {40 + R}} = {4 \over {400}} \Rightarrow R = 400 - 40 = 360\Omega $

Answer

220 $\Omega$

Answer

360 $\Omega$

Answer

760 $\Omega$

Answer

848.3 $\Omega$

Current Electricity

A potentiometer wire, 10 m long, has a resistance of 40\Omega. It is connected in series with a resistance box and a 4 V storage cell. If the potential gradient along the wire is 0.4 mV cm -1 , the resistance unplugged in the box is

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