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  4. The figure shows three conductors I, II and III of same material, different lengths l, 2 l and 3 l and of different areas of cross-section 3 A , A and 2 A respectively. Arrange them in the increasing order of current drawn from battery.

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Q. The figure shows three conductors I, II and III of same material, different lengths $l, 2 l$ and $3 l$ and of different areas of cross-section $3 A , A$ and $2 A$ respectively. Arrange them in the increasing order of current drawn from battery.Physics Question Image

Current Electricity

Solution:

As we know, resistance $R =\rho \frac{l}{A}$.
The resistance of conductor $l$ is given by
$R_l=\rho \frac{l}{3 A}=\frac{R}{3} \,\,\,\, \left(\right.$ where $\left.R=\rho \frac{l}{A}\right)$
Similarly, $R_{I I}=\rho \frac{2 l}{A}=2 R$
and $R_{l l l}=\rho \frac{3 l}{2 A}=\frac{3}{2} R$
From this we conclude that $R_{I I}>R_{I I I}>R_I$. Since in parallel combination of resistances current distributes in inverse ratio of resistances, therefore $i_2< i_3< i_1$.