First slide

Ohm's law

Question

In an electrical cable there is a single wire of radius 9 mm of copper. Its resistance is 5Ω . 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

45Ω
C

90Ω
D

270Ω

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
$R^{'} = ρ \frac{l}{π \times {(3 \times 10^{- 3})}^{2}}$ . Hence equivalent resistance of cable
$R_{eq} = \frac{R^{'}}{6} = \frac{1}{6} \times (ρ \frac{l}{π \times {(3 \times 10^{- 3})}^{2}}) . . . . (ii)$
On solving equation (i) and (ii) we get R_eq = 7.5 W

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