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A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R’, then find R/R’? |
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Answer» We know that, R ∝ l Initial resistance of the wire = RΩ When wire is cut into 5 pieces, its resistance will become 1/5th . ∴ resistance of each piece of wire after being cut into 5 pieces = \(\frac{R}{5}\)Ω Now, these wires are connected is parallel. ∴\(\frac{1}{R'}\) = \(\frac{1}{R_1} + \frac{1}{R_2}+\frac{1}{R_3}+\frac{1}{R_4}+\frac{1}{R_5}\) \(\frac{1}{R'}\) = \(\frac{1}{R/5}+\frac{1}{R/5}+\frac{1}{R/5}+\frac{1}{R/5}+\frac{1}{R/5}\) ∴\(\frac{1}{R'}\) = \(\frac{25}{R}\) ∴\(\frac{R}{R'}\) = 25 |
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