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Voltage and Current. Whenever positive and negative charges are separated, Voltage is the energy per unit charge created by the separation. Wherev = the voltage in volts w = the energy in joules q = the charge in coulombs. Voltage and Current (continued). - PowerPoint PPT Presentation
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ECE 201 Circuit Theory I 1
Voltage and Current
• Whenever positive and negative charges are separated,
– Voltage is the energy per unit charge created by the separation.
dwv
dq
Where v = the voltage in volts
w = the energy in joules
q = the charge in coulombs
ECE 201 Circuit Theory I 2
Voltage and Current (continued)
• The rate of charge flow is electric current
dqi
dt
Where i = the current in amperes
q = the charge in coulombs
t = the time in seconds
ECE 201 Circuit Theory I 3
Power and Energy
• Power is the time rate of expending or absorbing energy.
dwp
dt
Where p = the power in watts
w = the energy in joules
t = the time in seconds
1 Watt = 1 Joule/second
ECE 201 Circuit Theory I 4
Power Associated with the flow of charge
• Using the definitions of Voltage and Current
dw dw dqp
dt dq dt
p vi
Where p = the power in Watts
v = the voltage in volts
i = the current in amperes
ECE 201 Circuit Theory I 5
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
ECE 201 Circuit Theory I 6
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.
ECE 201 Circuit Theory I 7
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.
Battery12 V
HeadlightsKey = Space
Headlight_112V_25W
Headlight_212V_25W
Auto Chassis
AMMETER
DC 1e-009Ohm
0.000 A+ -
ECE 201 Circuit Theory I 8
Automobile Headlights (continued)
– Turn the headlights ON by closing the switch.
The headlights are ON. They draw a current of 4.138 Amperes from the battery.
Battery12 V
HeadlightsKey = Space
Headlight_112V_25W
Headlight_212V_25W
Auto Chassis
AMMETER
DC 1e-009Ohm
4.138 A+ -
ECE 201 Circuit Theory I 9
Jump Starting Example
• The current is measured to be 40 Amperes.
Which car has the dead battery?
ECE 201 Circuit Theory I 10
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.
ECE 201 Circuit Theory I 11
Problem # 1.15 part (b)
• If this connection is maintained for 1.5 minutes, how much energy is transferred to the dead battery?
tw(t) = pdx
0
1.5min = 90sec
90w(90) = 480dx
0
w = 480(90 - 0) = 43200J = 43.2kJ