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Question
A uniform wire of resistance 50 Ω is cut into 5 equal parts. These parts are now connected in parallel. The equivalent resistance of the combination is ______________ .
Options
2 Ω
10 Ω
250 Ω
6250 Ω
Solution
2 Ω
Resistance of a wire is directly proportional to its length.
So, when we cut the wire into 5 equal parts, the resistance of each part will be 10 Ω.
On connecting these wires in parallel, the net resistance will be
\[\frac{1}{R} = \frac{1}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} \]
\[ \Rightarrow R = 2 \Omega\]
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