Correct Answer - Option 3 : R/100 Ω
Concept: The property by which an electric conductor opposes the flow of current through it is called as the resistance of the conductor.
- It is denoted by R.
- The SI unit of resistance is Ohm (Ω).
\({\bf{Resistance}}\left( {\bf{R}} \right){\rm{}} = \frac{{\rho l}}{A}\)
Where ρ is the resistivity of the conductor, l is the length of the conductor and A is the cross-sectional area.
Explanation:
- When we stretch the wire then length increases but cross-sectional are decreases.
- But the total volume of the wire will remain constant.
- So we will write the formula of resistance in terms of volume (V).
Volume (V) = area (A) × length (l)
So A = V/l
\({\bf{Resistance}}\left( {\bf{R}} \right){\rm{}} = \frac{{\rho l}}{A}\)
Given that,
The resistance of a wire is proportional to its length R α L
The wire is cut into 10 equal parts. So, the resistance of each part = R/10
Then all 10 wires are connected in parallel. Then the equivalent resistance is
\(\frac{1}{R_{eq}}=\frac{1}{\frac{R}{10}}+\frac{1}{\frac{R}{10}}+.......\left ( 10\;times \right )\)
\(\frac{1}{R_{eq}}=\frac{100}{R}\)
The new resistance is \(R_{eq}=\frac{R}{100}\)
- Resistance can also be written as
\({\rm{Resistance}}\left( {\rm{R}} \right) = \frac{{\rho l}}{A} = \frac{{\rho l}}{{V/l}} = \frac{{\rho {l^2}}}{V}\)
