There is a dual of 8 ohm resistance on the aeria

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Solution

Q.
There is a dual of 8 ohm resistance on the aerial. Determine the aerial’s new resistance.

1 $2 Ω$

2 $4 Ω$

3 $7 Ω$

4 $10 Ω$

Ans.
(1)

Let ( l ) be the length and ( A ) be the area of cross-section.

$R = ρ \frac{l}{A} = 8 Ω l^{'} = \frac{l}{2} A^{'} = 2 A R^{'} = ρ \frac{l^{'}}{A^{'}} = ρ \frac{\frac{l}{2}}{2 A} = \frac{1}{4} (ρ \frac{l}{A}) = \frac{1}{4} \times 8 = 2 Ω$

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