Question

In a table like the one shown, write an inequality comparing each quantity in the steady state for a narrow resistor and thick connecting wires, which are made of the same material as the resistor.

Electron current in resistor	<,=, or >	Electron current in Thick Wires
nR		nw
AR		Aw
uR		uw
ER		Ew
vR		vw

Short answer

Electron current in resistor	<,=, or >	Electron current in Thick Wires
nR	=	nw
AR	<	Aw
uR	=	uw
ER	>	Ew
vR	>	vw

Step-by-step solution

Given data

A narrow resistor is connected in a circuit using thick connecting wires

Current in a circuit and drift velocity

Current in a wire of charge density , cross sectional area and drift velocity is given by:

$I=neAv$............(1)

Here, is the charge of an electron.

The drift velocity v as a function of the mobility u and the electric field E is$V=uE$............(2)

Comparison between quantities

The current in the circuit is the same everywhere in steady state. The electron density n and the mobility u are inherent properties of any material. Since the resistor and the wire are made of the same material, they have the same electron density and mobility, that is$$\begin{gathered} n_R=n_w \\ {u}_R=u_w \end{gathered}$$

The resistor is thin and the wire is thick. Thus the cross sectional area of the wire is greater than that of the resistor, that is$A_w>A_R$

Since cross sectional area of the wire is greater than that of the resistor, and current is same in both, from equation (1):

$v_R>v_w$

Thus, from equation (2):

$E_R>E_w$

The comparison in quantities can be summarized as

Electron current in resistor	<,=, or >	Electron current in Thick Wires
nR	=	nw
AR	<	Aw
uR	=	uw
ER	>	Ew
vR	>	vw