Question

How does the resistance depends upon length:
(A) Proportionally
(B) Inversely proportional
(C) Does not depends on length
(D) None of the above

Answer 1

Hint In the current electricity topic, there is relation which describes the dependence of resistance on several quantities. These quantities define the resistance of a wire and resistance of the wire will depend on length of wire, area of cross section of the wire and resistivity of the wire. Ideally we don’t consider temperature but it is also dependent on the temperature.

Complete step by step answer:
Dependence of quantities which define the resistance of conductor are:
Length: The resistance of a conductor depends on the length of the conductor. Actually, the resistance of a conductor is directly proportional to the length of the conductor.
Area: The resistance of a conductor dependent on the area of cross-section of the conductor/wire. The resistance of a wire is inversely proportional to the area of cross-section of the wire.
Material: The resistance of a wire depends upon the nature of material of the wire. Resistance of a wire is very less for those of aluminium and copper wires while resistance of a wire is maximum for rubber wires.
Temperature: The resistance of a wire depends on the temperature of the wire. Now, the nature of change of resistance depends on the material of the wire. For metal and alloys, the resistance of a wire increases on increasing the temperature of the wire. But in case of semiconductors like silicon and germanium used in electronic circuits, the resistance of these materials decreases on increasing the temperature of the wire.
So the relation of resistance with these quantities is:

Hence, option A is correct.

Note The relation of resistance with change in temperature is defined as:
\[R = {R_o}(1 + a\Delta t)\]
\[{R_o} = \] is the given resistance
\[R = \] is the new resistance
\[a = \] is the coefficient of thermal resistivity
\[\Delta t = \] is a change in temperature.