# Why is current same even if the area of the conductor differs?

Current is directly proportional to area if area of conductor increase Current increases but in tapering conductor area increases current remains same

I have learned this equation I=enAv Where A is area and v is drift velocity,as area increases does drift velocity decrease so that the current remains constant,does the density at smaller area increases which leads to increase in drift velocity or current remains constant with change in area as number of electron passing through cross section remains same at any velocity?

• Due to surface charges, if 2 wires are connected then the electric field value is different, making it constant May 19, 2022 at 17:25

(a) "Current is directly proportional to area" In general it isn't. It will be the same, though, when we connect the same voltage across wires of different cross-sectional area, but of the same length and material. In this case, $$n$$ and $$v$$ (and, of course, $$e$$) will be the same in the equation $$I=nAve$$.
(c) In the composite or tapering conductor (assumed homogeneous in material) the drift velocity $$v$$ adjusts to be greater where the conductor is thinner, so $$vA$$ is the same all along the conductor.
• Remember that $v$ is the so-called drift velocity, the mean rate of travel of free electrons in the direction of the applied electric field. It is superimposed on the much greater random thermal velocity of the free electrons. This means that the increase in drift velocity due to decrease in area of conductor makes only a very small change in the electron's velocity. I think that you $could$ regard it as an acceleration, but I'm on shaky ground because the motion of free electrons in a metal is strongly influenced by the forces between the electrons and the metal lattice. May 20, 2022 at 15:45