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(C) The drift velocity $v_d$ is given by the formula $v_d = \frac{I}{neA}$,where $I$ is the current,$n$ is the electron density,$e$ is the charge of a

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$3:2$

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(C) The drift velocity $v_d$ is given by the formula $v_d = \frac{I}{neA}$,where $I$ is the current,$n$ is the electron density,$e$ is the charge of an electron,and $A$ is the cross-sectional area.Since the wires are connected in parallel to the same battery,the potential difference $V$ across both wires is the same.Using Ohm's law,$I = \frac{V}{R}$,where $R = \rho \frac{L}{A}$. Thus,$I = \frac{VA}{\rho L}$.Substituting this into the drift velocity formula: $v_d = \frac{VA}{neA\rho L} = \frac{V}{ne\rho L}$.Since both wires are made of the same material,$n$,$e$,and $\rho$ are constant. Also,$V$ is constant.Therefore,$v_d \propto \frac{1}{L}$.The ratio of lengths is $L_1 : L_2 = 2 : 3$.Thus,the ratio of drift velocities is $\frac{v_{d1}}{v_{d2}} = \frac{L_2}{L_1} = \frac{3}{2}$.

The lengths of two wires made of the same material are in the ratio $2:3$ and their radii are in the ratio $1:2$. If the two wires are connected in parallel to a battery,then the ratio of the drift velocities of free electrons in the two wires is

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