Two cylindrical rods of uniform cross-section | vedclass

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(A) The current $I$ flowing through a conductor is given by the formula $I = n_e e A v_d$,where $n_e$ is the number of free electrons per unit volume,

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(A) The current $I$ flowing through a conductor is given by the formula $I = n_e e A v_d$,where $n_e$ is the number of free electrons per unit volume,$e$ is the charge of an electron,$A$ is the cross-sectional area,and $v_d$ is the drift velocity.Since the two rods are connected in series,the same current $I$ flows through both of them.For the left rod: $I = (2n) e A v_L$For the right rod: $I = (n) e (2A) v_R$Equating the two expressions for current:$(2n) e A v_L = (n) e (2A) v_R$$2 n e A v_L = 2 n e A v_R$Dividing both sides by $2 n e A$,we get:$v_L = v_R$Therefore,the ratio $\frac{v_L}{v_R} = 1$.

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