Current Electricity Charging Discharging Of Capacitors Question 132
Question: In an electrical cable there is a single wire of radius 9 mm of copper. Its resistance is $ 5,\Omega $ . The cable is replaced by 6 different insulated copper wires, the radius of each wire is $ 3,mm $ . Now the total resistance of the cable will be
[CPMT 1988]
Options:
A) $ 7.5,\Omega $
B) $ 45,\Omega $
C) $ 90,\Omega $
D) $ 270,\Omega $
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Answer:
Correct Answer: A
Solution:
Initially : Resistance of given cable $ R=\rho \frac{l}{\pi \times {{(9\times {{10}^{-3}})}^{2}}} $ … (i) Finally : Resistance of each insulated copper wire is $ R,’=\rho \frac{l}{\pi \times {{(3\times {{10}^{-3}})}^{2}}} $ . Hence equivalent resistance of cable $ R _{eq}=\frac{R,’}{6}=\frac{1}{6}\times ( \rho \frac{l}{\pi \times {{(3\times {{10}^{-3}})}^{2}}} ) $ … (ii) On solving equation (i) and (ii) we get Req = 7.5 W
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