Electric current

Electric Current Thermal energy flows from the hotter object to the colder object. Likewise, electrical energy is transferred from areas with higher potential to areas with lower potential. Careful! NOT necessarily individual charges

Quick rate of discharge If you touch a Van der Graaf generator with a wire also connected to the ground, the high potential of the charged dome would very quickly equalize with the ground. Shocking, but not always super useful.

Recycling charge? For most applications, recycling charges makes devices much more useful. To recycle charges, we need the equivalent of a pump somewhere in the circuit.

Pumps for charges? Charge only moves when there is potential difference Batteries chemical  electrical Generators mechanical  electrical We started the unit with voltage for a reason!

Danger? A Van der Graaf generator can build up a potential difference of 20,000 J/C. It’s shocking to touch but not typically dangerous. A car battery maintains a potential difference of just 12 J/C and will seriously harm or kill you if you complete the circuit with your body. Check this from UC Denver Med SchoolUC Denver Med School

Not the potential difference, but the current! Consider flow of water About the same potential difference A romantic spot for a swim with your special someone A disastrous spot for a swim with anyone

Electric Current The flow of water is measured in volume of water per unit time. The flow of electricity (current) is measured in charge per second, abbreviated as amperes or amps. second Coulomb = ampere or amp or A Named in honor of Andre-Marie Ampere (1775 – 1836) I = Q / t current = charge / time

Example In a certain light bulb, 3.0 C of charge pass through the filament in 5.0 s. What is the current in the light bulb? I = Q / t = 3.0 C / 5.0 s = 0.6 A Try it first. Move this box for the answer.

Example The current in a light bulb is 0.8 A. How long does it take for 1.6 C of charge to pass a point in the wire? I = Q / t So, t = Q / I = 1.6 C / 0.8 A = 20 s Try it first. Move this box for the answer.

Batteries A battery uses chemical means to cause charge to move continuously through a circuit. Alessandro Volta (1745 – 1827) invented the battery (1800) and described the work done by a battery per unit charge as the ‘electromotive force’, sometimes abbreviated emf and other times  (lower case epsilon)

Graphing potential in a circuit Suppose you connect a 9.0 V battery to a small motor. How does the electric potential change in the circuit? A B C D A B C D A voltage position battery wire motor wire battery

Graphing current in a circuit Suppose you connect a 9.0 V battery to a small motor. How does the current change in the circuit? A B C D A B C D A current position Charge does NOT get used up; the amount going in must equal the amount coming out

Graphing potential in a circuit Suppose you connect a 9.0 V battery to two small motors in series as shown below. How does the electric potential change in the circuit? A B C D A B C D E voltage position battery wire motor wire E F F motor wire

Graphing current in a circuit Suppose you connect a 9.0 V battery to two small motors in series as shown below. How does the current change in the circuit? ABCDE current position A B C D E F F Charge does NOT get used up; the amount going in must equal the amount coming out

Comparison In which situation would you expect the motor to spin faster? #1 #2

Graphing potential in a circuit Suppose you connect a 9.0 V battery to two small motors in parallel as shown below. How does the electric potential change in the circuit? A B C D A B C D A voltage position battery wire motor E F wire

Comparison 2 In which situation would you expect the motor to spin faster? #1 #2

Comparison 3 In which situation would you expect the battery to run down faster? #1 #2

Electric Power

Example It takes about 2 minutes for an electric heater in the US to bring 0.5 L of room-temperature water to a boil. Estimate the power of the heater. P=Q/t = mc  T/t = [(500 g) (4.2 J/g  C)(100  C-20  C)] / 120 s = 1,400 W Estimate the current through the heater. Note: most homes in the US have potential difference of 120 V P=IV, so I = P / V = (1,400 J/s) / (120 J/C) = 12 A Try it first. Move this box for the answer. Try it first. Move this box for the answer.

Example An electric heater draws a steady 15.0 A on a 120-V line. How much power does it require? P = I V = (15.0 C / s) (120 J / C) = 1800 W = 1.8 kW Try it first. Move this box for the answer.

Example If an 1800-W electric heater operates 3.0 h per day and operates for 30 days, how much does it cost to operate? Assume that the electric company charges $0.092 / kWh. Cost = ($ / kWh) (kW) (h) = ($0.092 / kWh) (1.8 kW) (3 h/day) (30 days) = $15 Try it first. Move this box for the answer.

Relationship between voltage and current Investigated by Georg Ohm, a German physicist (1787 – 1854)

Conductance and Resistance

Electrical Resistance Electrical resistance is Resistance is measured in ohms After Georg Ohm (1787 – 1854) Units: V per A = J / C per C / s = J s / C 2 Abbreviated with the Greek letter, omega,  current potential difference R = V / I

Ohm’s Law Check this link

Example A typical color television draws 2.5 A of current when connected across a potential difference of 115 V. What is the resistance of the television? R = V / I = 115 V / 2.5 A = 46  Try it first. Move this box for the answer.

Example A 1.5 V battery is connected to a small light bulb with a resistance of 3.0 . What current will it draw? I = V / R = 1.5 V / 3.0  = 0.5 A Try it first. Move this box for the answer.

Electric Power – pt 2

Electrical Resistance The current in a river depends on how quickly the water drops (potential difference) and cross section of the river. Likewise, the electrical current in a conductor depends on the voltage (potential difference) and the resistance.

Factors that affect electrical resistance Length of conductor  length   resistance Thickness of conductor  cross-sectional area   resistance Type of material  ‘grip’ on free electrons   resistance

Mathematical model for resistance Determined experimentally. Copper: 1.68 x  m Glass: 10 9  m Varies with temperature! Change in resistance  change in voltage  use electric current to measure temperature

Example Suppose you want to connect your stereo to remote speakers. If each wire must be 20 m long, what diameter copper wire should you use to keep the resistance less than 0.10  per wire? Resistivity of copper is 1.68 x  m. Try it first. Move this box for the answer.