Series Circuit
Same Current
 Two circuit elements joined
together end to start are in
series.
• One wire connection
I1
 Electrons don’t pile up in an
element as current flows.
 The two elements have the
same current.
• May have different voltage
I2
I1  I 2
Series Batteries
V1
V2
V3
Vser  V1  V2  V3
 Batteries can be joined in
series.
• Joined plus to minus
• Connecting lines are
conductors
 Total potential is the sum of
individual potentials.
V
• Normal battery symbol
suggests series
Series Resistors
R1
R2
R3
 Resistors can be joined in
series.
• End doesn’t matter
I
V  IR1  IR2  IR3
V  I R1  R2  R3 
V  IRser
 Ohm’s law gives the voltage
drop for each resistor.
• Sum for total
• Divide by current
 Total resistance is the sum of
individual resistances.
Rser  R1  R2  R3
Internal Resistance
 Real voltage sources have
some internal resistance.
• Resistor in series with battery
Rint
Vint
I
 The resistor reduces some
voltage from the battery.
• Same current through internal
resistance
• Ohm’s law for voltage drop
Veff
Veff  Vint  IRint
Power
 Power in a circuit is measured
in watts (W).
P
E E q

t q t
• Joule/sec
 A watt is a volt times an amp.
• Voltage times current
 Ohm’s law can be combined
with the power formula.
• Eliminate voltage or current
P  VI
P  I 2R
V2
P
R
Flashlight
 A flashlight uses a series circuit.
• Equivalent batteries and resistances
Lights On
 The flashlight uses two 1.5 V
batteries with 10 W internal
resistance each. The bulb has
a resistance of 50 W.
 Find the current through the
flashlight, and the power
dissipated by the bulb.
 The elements form a series
circuit.
• Total EMF of V = 3.0 V
• Total resistance of R = 70 W
 Ohm’s law gives the current.
• I = V/R = 3.0 V / 70 W
• I = 0.043 A = 43 mA
 The power is dissipated
through the resistors.
• P = V2 / R = 130 mW
Single Loop
Rint
Veff
Vint
I
 A circuit with a complete loop
is a closed circuit.
• All elements in series
• Interrupted circuit is open
 An ammeter measures current
Rint
Veff
Vint
I
A
and must be in series.
• Schematic symbol for amps
Kirchhoff’s Voltage Law
 An electron moving in a circuit loop has some potential
increases and some decreases.
• Increases from batteries, decreases from resistors
 The work done by the circuit on an electron in a closed
loop must be zero.
• Sum of potential changes must be zero
• Conservation of energy
 This is Kirchhoff’s voltage law.
V
i
loop
0
V   IR
i
batteries
resistors
j
0
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