Two wires A and B are of the same metal,have | vedclass

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Question

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

Vedclass · Accepted Answer

$1:2$

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(A) The resistance $R$ of a wire is given by the formula $R = \rho \frac{L}{A}$,where $\rho$ is the resistivity,$L$ is the length,and $A$ is the area of cross-section.Since both wires are of the same metal,their resistivity $\rho$ is the same. Given that $A$ is the same for both,$R \propto L$.Therefore,the ratio of resistances is $\frac{R_A}{R_B} = \frac{L_A}{L_B} = \frac{2}{1}$.According to Ohm's Law,$I = \frac{V}{R}$. Since the potential difference $V$ is the same for both,$I \propto \frac{1}{R}$.Thus,the ratio of currents is $\frac{I_A}{I_B} = \frac{R_B}{R_A} = \frac{1}{2}$.

Two wires $A$ and $B$ are of the same metal,have the same area of cross-section,and have their lengths in the ratio $2:1$. What will be the ratio of currents flowing through them respectively,when the same potential difference is applied across each of them?

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