Chapter 20
Electric Circuits
1
20.1 Electromotive Force and Current
DC =
A typical DC circuit
Direct
Current
I→
DC
Electric
Power
Source
I→
Working
Device
E
E
R
schematic diagram
←I
←I
Power Source:
Working device:
Boosts electric
potential energy of
charge carriers by
qE each
Converts energy carried by charges into
work, heat or other forms of energy
+
+
+
q
I→
+
+
+
Current:
flow of
charge
E
− +
+
+
+
+
←I
+
+
+
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20.1 Electromotive Force and Current
+
E
−
Symbol for a DC
voltaic cell
E=electromotive force (emf)
Potential by which the
(positive) charge carriers are
raised
Typical car battery:
6 x 2V lead-acid
cells  E =12V
−
Units: volts
+
Both are exothermic reactions
Symbol for a multi-cell
battery (showing 5 cells)
+
−
The electric current = amount of charge per unit time
passing through a surface ⊥ motion of charges.
Current
∆q
I=
∆t
One ampere (A or amp). = one coulomb per second: 1 A = 1 C/s
Direct Current (DC):
Charges move in the
same direction at all
times
If the charges move first
one way and then the
opposite way, the current
is said to be alternating
current (AC).
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20.1 Electromotive Force and Current
Conventional current is the hypothetical flow of positive charges that
would have the same effect in the circuit as the movement of negative
charges (electrons) that actually does occur in the opposite direction.
Example A Pocket Calculator
The current in a E=3.0V battery of a pocket calculator is I=0.17mA. In
one hour of operation,
(a) how much charge flows in the circuit and,
(b) how much energy does the battery deliver to the calculator circuit?
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20.1 Electromotive Force and Current
Example A Pocket Calculator
Conventional current is the hypothetical
The current in a E=3.0V battery of a
pocket calculator is I=0.17mA. In one
hour of operation,
flow of positive charges that would have the
same effect in the circuit as the movement of
negative charges (electrons) that actually
does occur in the opposite direction.
(a) how much charge flows in the circuit
and,
(b) how much energy does the battery
deliver to the calculator circuit?
(a)
∆q = I (∆t )
= (0.17 × 10 −3 A )(3600 s )
= 0.61 C
+
+
+
e−
e−
e−
e−
(b)
Energy = Charge ×
Energy
Charge
E = q( ∆V )
+
= (0.61 C )(3.0 V )
= 1.8 J
5
20.2 Ohm’s Law
I→
Symbol for a multi-cell
battery (showing 5 cells)
E
←I
R
Ohm’s Law
I ∝V
V
V
= R = Resistance, V = IR, or I =
I
R
Conductors in general obey Ohm’s Law. Those materials we use to
connect circuit elements (wires/cables/traces) have very low resistance
(generally not measurable with hand-held meters). We generally treat
them as if they have no resistance at all. The components with
measurable resistances are referred to as “resistors”
SI Unit of Resistance:
volt/ampere (V/A)
= ohm (Ω)
Symbol for a resistor
R
6
20.2 Ohm’s Law
Example: Flashlight
The filament in a light bulb is a resistor in the form of
a thin piece of wire. The wire becomes hot enough to
emit light because of the current in it. The flashlight
uses two 1.5-V batteries (stacked in series) to provide
a current of 0.40 A in the filament. Determine the
resistance of the glowing filament.
7
20.2 Ohm’s Law
Example: Flashlight
The filament in a light bulb is a resistor in the form of
a thin piece of wire. The wire becomes hot enough to
emit light because of the current in it. The flashlight
uses two 1.5-V batteries (stacked in series) to provide
a current of 0.40 A in the filament. Determine the
resistance of the glowing filament.
NOTE:
(1) V = ∆V = Vu−Vd
V
3.0 V
R= =
= 7.5 Ω
I 0.40 A
specifically the upstream
potential minus the
downstream potential
(2) Potential is measured at
ONE point on the circuit.
Potential difference is
measured between TWO
points in a circuit.
(3) Current is measured
THROUGH a continuous
segment of a circuit (i.e.
no branch points)
Vu
V=∆V
Vd
R
+
+
I
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20.3 Resistance and Resistivity
For a wide range of materials, the resistance of a piece of material depends on both the
intrinsic properties of the material as well its size and shape. In particular, resistors are
usually shaped in the form of a bar of length L and cross-sectional area A is given by:
V
L
R=ρ
A
I
ρ
A
resistivity (in units of ohm·meter)
is an intrinsic (but temperaturedependent) property of a material
Water-flow analogy of electrical
circuit:
pump ↔ battery
pressure ↔ potential
pipes ↔ wires
constriction ↔ resistor
the narrower the constriction, the
higher the resistance to flow
The longer the constriction, the
higher the resistance
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