Voltage and Current

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