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Question
A wire of resistance 9 ohm having length 30 cm is tripled on itself. What is its new resistance?
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Solution
Resistance (R) = 9 ohm
Length l = 30 cm
New Length (l) = 30 cm = `l/3` = 10 cm
New area an = 3a
`R = ρ 1/a`
Initial resistance `9 = ρ 30/a` ...(i)
New resistance `R_n = ρ 10/(3a)` ...(ii)
On dividing eqn (ii) by (i), we get,
`R_n/9 = (ρ 10/(3a))/(ρ 30/a)`
`R_n /9 = 10/90`
`R_n /9 = 1/9`
`R_n /1 = 9/9`
Rn = 1 Ω
Hence, The new resistance = 1 ohm.
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