| Convention |
Notes |
| Conventional current is positive current. |
We now know--unlike
in Ben Franklin's day--that electric current is due to the movement of
electrons; hence, electrical current is negative current. Ben Franklin
didn't know that and assumed the opposite. His convention stuck and so
now we conventionally talk about current as the movement of positive
charge even though we know otherwise. The physics still works out as
long as we make the direction of positive current opposite that of
electron current. Generally, when we just say current without an
adjective, we mean conventional (positive) current. Note that inside a
battery, the direction of positive current is from the negative to the
positive terminal while in the circuit outside the battery, positive
current goes from positive to negative. |
| The
symbol I represents conventional current. |
This doesn't mean, however, that you
can't get negative values for I. If you solve a
circuit problem and I comes out negative, that may just mean that
the conventional current is in the opposite direction as you thought. |
| Represent potential difference with a symbol that
means change, namely, ΔV. |
You'll find that the
textbook often uses the symbol V to represent potential difference
(sometimes called voltage for short). However,
it makes more sense to represent potential difference explicity as a change, ΔV. This
represents the difference of potential between two points in a circuit.
If the points are a and b, then another way to write this
is ΔV = Vba = Vb - Va.
This makes it clear that potential difference can be positive or
negative. Note that inside a battery, the potential rises from the
negative to the positive terminal while in the circuit outside the
battery, potential falls from positive to negative. |
Electrical resistance is always positive. |
The definition of electrical resistance is R = -ΔVr/I. How do you get a positive number out of that? Well, when positive
current passes through a resistor, the change of potential, ΔVr, across the
resistor is negative. Therefore, -ΔVr is positive. |
| Quantity |
Symbol |
Defining Formula |
SI Units |
Notes |
| Current |
I |
I = Q/t |
C/s or A |
Conventional current is taken
to be positive current. |
| Potential Difference |
ΔV or Vba |
ΔV = ΔUel /Q |
V |
Potential difference is the
change in electrical potential energy per unit charge as charge Q moves from point to point in a circuit. This is referred to as
voltage and represented by V in the textbook under the
assumption that the lower potential is always 0. In your problem
solutions and lab work, avoid use of the naked V symbol. |
| Resistance |
R |
R = -ΔVr /I |
Ω |
Since ΔVr across a
resistor is negative (from + to -) and current is positive (from
+ to -), the quantity R = -ΔVr /I is always positive. |
| Relationship |
Notes |
| Conservation of
charge |
The fact that charge is
conserved leads to the conclusion that the current is the same
in all parts of a single loop circuit. From the definition of
current, I = Q/Δt. For a given Δt, equal charge means
equal current. |
| Conservation of
energy |
The total change in electric
potential energy ΔUel around a circuit is 0.
All the energy produced by the battery is used in the circuit.
Now ΔUel = QΔV, where ΔV is the difference potential
around the circuit. But the difference of potential in returning
to the same point must be 0. Another way of saying this is that
the algebraic sum of all the potential differences around a
circuit must be 0. This is simply an expression of conservation
of energy. |
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