Voltage and Current
• Whenever positive and negative charges are
separated,
– Voltage is the energy per unit charge created by the
separation.
v
Where
dw
dq
v = the voltage in volts
w = the energy in joules
q = the charge in coulombs
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Voltage and Current (continued)
• The rate of charge flow is electric current
i
Where
dq
dt
i = the current in amperes
q = the charge in coulombs
t = the time in seconds
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Power and Energy
• Power is the time rate of expending or absorbing energy.
p
dw
dt
Where p = the power in watts
w = the energy in joules
t = the time in seconds
1 Watt = 1 Joule/second
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Power Associated with the flow of charge
• Using the definitions of Voltage and Current
dw dw dq
p

dt
dq dt
p  vi
Where
p = the power in Watts
v = the voltage in volts
i = the current in amperes
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The Basic Ideal Circuit Element
• The ideal basic circuit element
– has only two terminals
– is described mathematically in terms of current and/or
voltage
– Cannot be subdivided into other elements
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Passive Sign Convention
If the power is positive (p>0), power is being delivered to the
circuit inside the box. If the power is negative (p<0), power is
being extracted from the circuit inside the box.
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Circuit Theory
• What is an electric circuit?
– A mathematical model that approximates the behavior of an
actual electrical system.
• Example: Automobile Headlights
– Here the headlights are OFF and draw no current from the
battery because the switch is open.
Headlights
Key = Space
AMMETER
+
0.000
A
DC 1e-009Ohm
Battery
12 V
Headlight_1
12V_25W
Headlight_2
12V_25W
Auto Chassis
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Automobile Headlights (continued)
– Turn the headlights ON by closing the switch.
Headlights
Key = Space
AMMETER
+
4.138
A
DC 1e-009Ohm
Battery
12 V
Headlight_1
12V_25W
Headlight_2
12V_25W
Auto Chassis
The headlights are ON. They draw a current of 4.138 Amperes
from the battery.
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Jump Starting Example
• The current is measured to be 40 Amperes.
Which car has the dead battery?
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The current is flowing into the + terminal of the battery
in car A.
p = vi = (12V)(40A) = 480W
Since the power is positive, the battery in car A is
absorbing power. Car A has the dead battery.
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Additional Calculation
• If this connection is maintained for 1.5 minutes, how
much energy is transferred to the dead battery?
t
w(t) =  pdx
0
1.5min = 90sec
90
w(90) =  480dx
0
w = 480(90 - 0) = 43200J = 43.2kJ
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