Question

Which has more resistance:
(a) a long piece of nichrome wire or a short one?
(b) a thick piece of nichrome wire or a thin piece?

Answer 1

Hint: Resistance and resistivity are related terms but with quite a little difference. This difference is of great importance in understanding the factors affecting resistance. Similarly, one of such factors is dimension. For better understanding of this factor, we need to be aware of the numeric relation between resistance and resistivity.

Complete step by step answer:
Resistance and Resistivity are related to each other as
$R = \dfrac{{\rho l}}{A}$
Where, R = Resistance, l = length, A = Area, $\rho $= Resistivity.
From the above formula we can conclude that,
$R\,\propto \,l$
$\Rightarrow R\,\propto \,\dfrac{1}{A}$
We can write it as, resistance of the object is directly proportional to the length and inversely with the area covered by the object. Hence with increase in length the resistance of the object will also increase. So, we can conclude that a long piece will offer more resistance.

Area of any object is directly proportional to radius of that object. With increase in the object’s thickness, we can observe an increase in radius as well as the area of the object. So, a thick piece of nichrome will have a larger area than a thin piece of nichrome.As resistance is inversely proportional to area of object hence, we can conclude that a thick piece will have a smaller resistance than a thin piece of nichrome.
(a) A long piece of nichrome wire offers more resistance than a short wire.
(b) A thin piece of nichrome wire offers more resistance than a thick wire.

Note: Hindrance in the flow of anything is termed as resistance and is basically used as the term resistance in electric conduction. In different types of flow the resistance is termed with different names such as viscosity in the liquid flow system.