Question 27: 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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