Electric potential and
Voltage
The exact path and instantaneous speed of the skier on the slope
depends on path shape, steepness, length etc.
But the final skier speed only depends on the potential energy difference between the top and the bottom points of the slope:
Wtop = mgHtop; Wbot = mgHbot; v
=
2
gH
−
gH
2
top
bot
Wtop ‐ Wbot = mv /2;
(
)
Note: 1) there is NO absolute height: it is taken with respect to some reference point (e.g. the sea level) 2) the velocity v depends on the height difference only!
­
+
Similarly, the electric current only depends on the electric potential energy difference between the terminals
Electric potential
Potential is the electric potential energy of a unit charge.
Potential is measured in Volts (V)
1V is the potential that provides a potential energy of 1 J (Joule) to the unit charge of 1C (Coulomb).
1J
1V =
1C
If the potential ϕ is known, the potential energy of any charge Q can be found: WE = Q ×
ϕ
Note that the potential is always measured with respect to some reference point (so­called “ground node”) in the circuit A
B
­
+
The terminal B is 9 V more positive than the terminal A.
Equivalent statement: the potential of the point B is 9V higher than that of point A.
Equivalent statement:
The electric energy of a positive charge of 1 C at point B is 9 J higher than that of the same charges at point A.
B
A
The 24 V battery is connected to a 5 Ω resistor as shown.
Assume all the wires are ideal: no energy needed to move the charge along the wire, hence zero voltage across the wire.
Let point A be grounded (zero potential).
The potential of point B is:
+24 V
B
A
Let point B be grounded (zero potential).
The potential of point A is ‐24 V
Voltage
ϕ1
ϕ2
The current depends only on the potential difference between the terminals.
For example, if ϕ1 = 100 V and ϕ2 = 100 V (both fairly high!)
the current through the resistor R is ZERO
because there is no electric field and electric force across this resistor.
However, if ϕ1 ≠ ϕ2, the current is flowing through the resistor R.
Voltage
Voltage = Potential Difference
Being a potential difference, voltage is also measured in Volts (V)
Voltage can only be defined for two points (nodes, terminals etc.)
Voltage of a single node in the circuit does not make sense.
Potential can be used to characterize a single node provided that the zero (ground) node is defined.
For two points 1 and 2 with the potentials ϕ1 and ϕ2 in a circuit, the voltage V21 between the point 2 and point 1: V21 = ϕ2 ‐ ϕ1
the voltage V12 between the point 1 and point 2: V12 = ϕ1 – ϕ2= ‐
V21
Example
2
1
3
0
The three nodes, “1”,”2”,”3”
in the amplifier circuit have the potentials
ϕ1 = 3 V; ϕ2 = 9 V; ϕ3 = 6.5 V with respect to the reference node “0”
Question 1: find the voltages V21, V32, V31 and V13
Solution: Vmn = φm ­ φn
V21 = ϕ2 – ϕ1 = 9V – 3V = 6 V;
V32 = ϕ3 – ϕ2 = 6.5 V – 9V = ‐2.5 V;
V31 = ϕ3 – ϕ1 = 6.5V – 3V = 3.5 V;
V13 = ϕ1 – ϕ3 = 3V – 6.5V = ‐3.5 V;
B
D
C
+
+
­
­
A
In this circuit, point A is grounded (zero potential).
The potential of point B is +28 V
The potential of point C is +7 V
Suppose that the potential of the point D is 10 V.
What is the voltage VDB across R1?
What is the voltage VDC across R3?
What is the voltage VCD?
What is the voltage VDA across R2?
What is the voltage VBC?
B
D
C
+
+
­
­
A
In this circuit, point A is grounded (zero potential).
Suppose that the voltage VDB is ‐10 V.
What is the potential of the point D?
What is the voltage VDC?
B
D
C
+
+
­
­
A
In this circuit, point A is grounded (zero potential).
The potential of point B is +28 V
The potential of point C is +7 V
Suppose that the potential of the point D is 10 V.
What is the direction of the current flowing through R1?
What is the direction of the current flowing through R2?
What is the direction of the current flowing through R3?