Question

A hank of uninsulated wire consisting of seven and a half turns is stretched between two nails hammered into a board to which the ends of the wire are fixed. The resistance of the circuit between the nails is determined with the help of electrical measuring instruments. Determine the proportion in which the resistance will change if the wire is unwound so that the ends remain to be fixed to the nails
A) 225
B) 15
C) 240
D) 250

Answer 1

Hint:The problem is from the current electricity part of physics. We can apply the concept of resistance here. Use the equation for effective resistance in parallel and series combinations. The equivalent resistance is a single resistance which can replace all the component resistances in a circuit in such a manner that the current in the circuit remains unchanged.

Formula Used:
Equivalent resistance for a series resistance circuit:
${R_E} = {R_1} + {R_2} + {R_3}$
Where ${R_E}$= equivalent resistance and ${R_1},{R_2},{R_3}$ = component resistance.
Equivalent resistance for a parallel resistance circuit:
$\dfrac{1}{{{R_E}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}}$
Where ${R_E}$= equivalent resistance and ${R_1},{R_2},{R_3}$ = component resistance.

Complete answer:
The uninsulated wire consists of 7.5 turns. Let resistance of a half turn = R.
Then in the first case, the 15 resistors of resistance R are connected in parallel combination. So, the equivalent resistance will be ${R_E} = \dfrac{R}{{15}}$.
In the second case, the 15 resistors of resistance R are connected in a series combination. So, the equivalent resistance will be ${R_E} = 15R$.
After unwinding, the resistance will increase by ${15^2} = 225$

Hence, the correct option is Option (A).







Note: A conductor's electrical resistance is affected by the following parameters: The conductor's cross-sectional area, the conductor's length, the conductor's material and the conducting material's temperature. Electrical resistance is inversely proportional to the cross-sectional area and directly proportional to the conductor's length.