Question 309: Current Electricity

Question

A Copper (Cu) rod of length 25 cm and cross-sectional area 3 mm
2
is joined with a similar Aluminium (Al) rod as shown in figure. Find the resistance of the combination between the ends A and B.
(Take Resistivity of Copper = 1.7 $$	imes$$ 10
$$-$$8
$$\Omega$$m and Resistivity of Aluminium = 2.6 $$	imes$$ 10
$$-$$8
$$\Omega$$m)

Accepted Answer

$${R_{Cu}} = {{{ho _{Cu}} 	imes l} \over A}$$
$${R_{Al}} = {{{ho _{Al}} 	imes l} \over A}$$
$${R_{Eq}} = {{{ho _{Cu}} 	imes {ho _{Al}}} \over {{ho _{Cu}} + {ho _{Al}}}} 	imes \left( {{l \over A}} ight)$$
$$ = {{1.7 	imes {{10}^{ - 8}} 	imes 2.6 	imes {{10}^{ - 8}}} \over {(1.7 + 2.6) 	imes {{10}^{ - 8}}}} 	imes {{0.25} \over {3 	imes {{10}^{ - 6}}}}$$
$$ = 0.856$$ m$$\Omega$$

Answer

0.0858 m$$\Omega$$

Answer

1.420 m$$\Omega$$

Answer

0.858 m$$\Omega$$

Answer

2.170 m$$\Omega$$

Current Electricity

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