Electric Current

Any electric charge placed in electric field F experiences an

electric force = q × F

F

q

If there is a potential difference between

two points, the electric field exists in the

space between them

Electric Field makes mobile charges moving

F

q

If the charge is “free” or “mobile”, then in the electric field it

would move (“drift”) pushed by the electric force.

The charge drift velocity,

v = µµµµ × F,

Here µµµµ is a coefficient called “mobility”

Electric Field causes Electric Current in

conductors

F

q

“Conductor” is any material that contains a lot of “free” or

“mobile” charge.

When a conductor is placed in an electric field, the mobile

charges in it start moving (“drifting”).

Moving mobile charges form an electric current

Electric Current

�Electric current is the rate of electric charge transfer.

�Electric current is measured as the charged transferred through any cross-

section of the conductor per unit time

t

QI

∆

∆=

∆Q is the charge crossing the reference plane of a

conductor per time ∆t

q

Electric Current

Example 1

If each marble is charged and carries the electric charge 0.1 C

and 10 marbles pass through the open end of the tube per 1 second,

the current is

( )0 1 101 1

1

CChargeI C s A

Time s

×= = = =

./

1 1A C s= /

Current is measured in Amperes:

Electric Current

Example 2

Consider a nano-tube filled with a fluid.

The fluid contains positively charged mobile molecules.

There are 105 charged molecules per 1 cm of the nano-tube length.

Each molecule has a charge of +1.6 ×10-19 C.

In applied field, the molecules move with the

drift velocity v = 103 cm/s.

What is the electric current through the nano-tube?

Electric Current

Example 2

Consider a 1 cm-long part of the nano-tube.

Let us calculate the charge transferred through the plane A.

In the 1 cm long part, there are 105 charged molecules.

How long does it take them to pass the plane A?

The last molecule has the longest way to go. For it, the time to reach

the plane A is: Distance/Velocity = 1 cm/ (103 cm/s) = 10-3 s.

By that time, all the molecules within that 1 cm will pass the plane A

1 cm

A

Electric Current

Example 2

Therefore, in 10-3 s, 105 molecules would cross the plane A.

What charge is transferred by those molecules?

Each molecule carries the charge +1.6 ×10-19 C. Hence, the total

transferred charge, ∆Q = 1.6 ×10-19 C × 105 = 1.6 ×10-14 C.

The time it takes to transfer this charge, ∆t = 10-3 s.

Hence, the current is: I = ∆Q / ∆t = 1.6 ×10-11 A.

Answer: the current I = 1.6 ×10-11 A

1 cm

A

Electric Current

Example 3

A metal wire contains 1014 free electrons per 1 cm of the wire

length.

Each electron has an electric charge of -1.6 ×10-19 C.

The electric field accelerates the electrons to the drift velocity

v = 104 cm/s.

What is the electric current in the wire?

Electric Current

Example 3

As follows from the previous example,

Current, I = (the charge of a single mobile electron, e) ×

(number of electrons per unit length of the wire, N1) ×

(electron velocity, v).

I = 1.6 ×10-19 C × 1014 cm-1 × 104 cm/s = 0.16 C/s = 0.16 A

I = e × N1 × v

e N v

Electric Current

STOP !

Is there an error in the above calculations?

The electron charge is NEGATIVE: - 1.6 ×10-19 C

Shouldn’t the current be negative

I = -1.6 ×10-19 C × 1014 cm-1 × 104 cm/s = -0.16 C/s = -0.16 A ?I = -e × N1 × v

e N v

q+

Electric Current Direction

Let’s take “x” axis in the direction of the electric field .

The current, I = q × N1 × v

q is the charge of a single mobile charged particle,

N1 is the number of particles per unit length,

v is the particle velocity in the electric field.

x

v

Electric Current Direction -2

v

q+

Suppose that the conductor contains positive mobile

charges (e.g. ionized molecules of electrolyte).

Positive charges move from “+” to “-” - in the same

direction as the electric field, i.e. the velocity v is positive.

Electric Current Direction -2

v

q+

Therefore, for positively charged particles we have:

q > 0 ; v > 0;

The current, I = q × N1 × v; hence I > 0

The current created by positive charges is positive

Electric Current Direction -4

v

q

Suppose that the conductor contains

negative mobile charges (e.g. electrons).

Negative charges move from “-” to “+” - in the direction

opposite to that of electric field, i.e. the velocity is negative:

v < 0 .

-

x

Electric Current Direction - 5

Therefore, for the current created by negative charges we

have:

q < 0 ; v < 0;

The current, I = q × N1 × v; “-” × “-” = “+”, hence I > 0

The current created by positive charges is positive

x

v-

No matter what the type of the mobile charges in the

conductor is (positive or negative),

the direction of electric current is always from the

positive terminal toward the negative terminal.

More common short form of this statement:

the current flows from “+” to “-”

If the conductor contains both positive and negative

charges, the total current is the sum of the two component.

Electric Current direction summary

Timed response

Example problem 1

If a current of 10 mA passes through your cell phone battery charger

wire for 10 minutes, what quantity of electric charge is transferred

through the wire to the battery?

0

of

5

120120

Example problem 1 - solution

∆Q = I × ∆t

∆Q = (10*1E-3) A* (10 * 60 s) = 6 C

If a current of 10 mA passes through your cell phone

battery charger wire for 10 minutes, what quantity of

electric charge is transferred through the wire to the

battery?

Example problem 2

How much current does your laptop consume if 100 C of charge

is transferred through the charger wire in 4 seconds?

120120

0

of

5

Timed response

Example problem 2 - Solution

I = ∆Q/ ∆t

I = 100 C/ 4 s = 25 A

How much current must there be in your laptop if 100 C is

transferred through the charger wire in 4 seconds?

Example problem 3

How much time is required for 10 Coulombs of charge to flow past a

point if the current is 2 amperes?

6060

1. 5 s

2. 20 s

3. 20 min

4. 5 min

Timed response

How much time is required for 10 Coulombs of charge to

flow past a point if the current is 2 amperes?

Example problem 3 - Solution

I = ∆Q/ ∆t

∆t = ∆Q/ I

∆t = 10 C/ 2 A = 5 s

Example problem 4

Example problem 4

A conductor has a constant current of 5 A. How many electrons

pass through a cross-section of the conductor in 3 minutes?

120120

0

of

5

Timed response

A single electron charge is q = 1.6 × 10-19 C (we can ignore the

sign as we only need the number of electrons).

If N electrons pass through the conductor,

the total charge transferred: ∆Q = N × q.

If the time needed for the charge to pass through is ∆t,

then the current is: I = ∆Q/∆t = N × q/∆t;

From this, the number of electrons: N = I × ∆t/q.

∆t = 3 min. = 3 ×60 s = 180 s.

N = 5 A ×180s/ 1.6 × 10-19 C =

= 5.625 × 1021 electrons

Answer: N = 5.625 × 1021 electrons

A conductor has a constant current of 5 A. How many

electrons pass through a cross-section of the conductor in 3

minutes? Solution.

Example problem 5

0

of

5

6060

A bath with a liquid electrolyte is connected to the battery.

The electrolyte has positive and negative mobile ions in it.

The current carried by positively charged ions is 12 mA.

The current carried by negatively charged ions is 7.5 mA.

What is the total current flowing through the electrolyte?

Timed response