First slide

combination of resistance

Question

In an electrical cable there is a single wire of radius 9 mm of copper. Its resistance is 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

Moderate

A

$7.5 Ω$
B

$45 Ω$
C

$90 Ω$
D

$270 Ω$

Solution

Initially : Resistance of given cable
$R = ρ \frac{l}{π \times {(9 \times 10^{- 3})}^{2}}$ …..(i)
Finally : Resistance of each insulated copper wire is
$R^{'} = ρ \frac{l}{π \times {(3 \times 10^{- 3})}^{2}}$ = 9R
Hence, equivalent resistance of cable
$R_{eq} = \frac{R^{'}}{6} = \frac{1}{6} \times (ρ \frac{l}{π \times {(3 \times 10^{- 3})}^{2}})$ = $\frac{9 R}{6}$ ….(ii)
On solving equation (i) and (ii) we get $R_{e q} = 7.5 Ω$

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