Electric Current
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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
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