A metal rod of length 10 text{ cm} and a rect | vedclass

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Question

(A) The resistance of a conductor is given by the formula $R = \rho \frac{l}{A}$, where $\rho$ is the resistivity, $l$ is the length of the conductor

Vedclass · Accepted Answer

Maximum when the battery is connected across $1 	ext{ cm} 	imes 0.5 	ext{ cm}$ faces.

Vedclass · Answer

(A) The resistance of a conductor is given by the formula $R = ho \frac{l}{A}$, where $ho$ is the resistivity, $l$ is the length of the conductor in the direction of current flow, and $A$ is the cross-sectional area perpendicular to the current flow.To maximize the resistance $R$, we need to maximize the length $l$ and minimize the cross-sectional area $A$.When the battery is connected across the $1 	ext{ cm} 	imes 0.5 	ext{ cm}$ faces, the current flows along the length of $10 	ext{ cm}$. Thus, $l = 10 	ext{ cm}$ and $A = 1 	ext{ cm} 	imes 0.5 	ext{ cm} = 0.5 	ext{ cm}^2$.The resistance is $R = ho \frac{10}{0.5} = 20ho$.For the other two orientations, the length $l$ will be either $1 	ext{ cm}$ or $0.5 	ext{ cm}$, and the area $A$ will be larger, which results in a smaller resistance value.Therefore, the resistance is maximum when the battery is connected across the $1 	ext{ cm} 	imes 0.5 	ext{ cm}$ faces.

$A$ metal rod of length $10 \text{ cm}$ and a rectangular cross-section of $1 \text{ cm} \times 0.5 \text{ cm}$ is connected to a battery across opposite faces. The resistance will be . . . . . . .

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