a wire whose cross sectional area is increasing linearly is connected across a battery of v volts. Which of these remaim constant and why?
1.drift speed
2.current density
3.current
4.electric field.
Answers
A wire whose cross sectional area is increasing linearly is connected across a battery of v volts. Which of these remain constant .
1.drift speed
2.current density
3.current
4.electric field.
current is directly proportional to area , so the value of drift speed changes.
Current density remains constant as it is independent of area.
Voltage= current × resistance
Resistance R= resistivity×length÷area.
current is proportional to area.
current density=current÷area.
current density is independent of area.
So current density remains constant.
Current I=neA×drift velocity.
Current is directly proportional to area from ohms law if voltage remains constant, which implies drift velocity is independent of Area.
The dependance of drift velocity on area can be explained based on the below reason
The drift velocity does not depend on the length or the cross sectional area of the wire, when dealing with a macroscopic (ordinary, everyday life) wire. However, if the wire is, say, too short, e.g. comparable to the average distance a charge carrier travels before undergoing a collision, then it might begin to depend on the wire length, but for all practical intents and purposes a wire won't be that short.
The reason v does not depend on the wire cross sectional area is that the ratio I/A is constant (assuming the applied electric field within the wire is not changing), also called the current density, denoted by J=I/A. So, for example, if A doubles, I will also double (wire capacity doubles), keeping J constant.
The elecric field is not varied by any changes in the cross-sectional area. You can make sure of it by taking a look at Electric Field’s formula. It depends only on : distance of the point from source charge ; magnitude and sign of source charge.
Current density and electric field and drift velocity remains constant as they are independent of area, while the remaining quantities depends on area and their value changes.