I Q The electric current, I, is the rate of flow of charge Q through a given area in a given amount of time in an electric conductor. Units: Coulomb/second = Ampere (A) Current = charge time Andre M. Ampere

q = (6 A)(3 s) = 18 C Recall that: 1 e - = 1.6 x C, then convert: In 3 s: 1.12 x electrons Example 1. The electric current in a wire is 6 A. How many electrons flow past a given point in a time of 3 s? I = 6A t = 3 s e- = ?

Conventional Current vs Electron Flow theory OR Physics vs Chemistry Which way does the current go?Which way does the current go? :

Electron flow: Current flows in the direction an e - moves; from – to +. Conventional current: Current flows in the direction a +q moves; from + to – Electron flow e-e-e-e- Conventional flow + Q = CV Imagine a charged capacitor with Q = CV that is allowed to discharge

SOOOO. We will use conventional current as our preferred method for describing the flow of current in a circuit. In a wire (a conducting metal), electrons are the only charged particles moving in an electrical current.

A source of electromotive force (emf) is a device that converts, chemical, mechanical, or other forms of energy into the electric energy necessary to maintain a continuous flow of electric charge. The source of the emf in this case is chemical energy.

Example: Fred’s portable DVD player draws 0.600A of current. If new batteries supply 6400 C of charge until they run out, how long does the DVD player run? I = A Q= 6400 C t = Q I = 6400 C C/s = 10,666 sec If the DVD player used 3V, how much energy does the battery use to run the player? V = W q o W = Vq o = (3V)(6400 C) = 19,200 J

Resistance Resistance is an opposition to the flow of charge Resistors

A resistor in a circuit is ANYTHING that opposes the flow of the current or uses voltage This includes the wires of the circuit.

RESISTIVITY The resistance of a wire of uniform cross-sectional area is determined by: The kind of material The length The cross-sectional area The temperature ρresistivity l mA Where ρ is the resistivity of the material in Ω.m, l is the length in m, and A is the cross-sectional area in m 2.

Digit – digit - multiplier 10 X 4 band resistors Orange – Black - Brown 3 0x 10Ω 300 Ω More practice later! later!

Example: What is the resistance of a 20 m length of copper wire with a diameter of 0.8 mm? ρ = 1.72x10 -8 Ω.m l = 20 m r = d/2 = 4x10 -4 m A = πr 2 = π(4x10 -4 ) 2 = 5.02x10 -7 m Ω = Ω

"For a given resistor at a particular temperature, the current is directly proportional to the applied voltage." ohm Units: Volt/Amperes = ohm (Ω) Georg Simon Ohm ( )

Example: The voltage between the terminals of an electric heater is 80 V when there is a current of 6 A in the heater. What is the current if the voltage is increased to 120 V? V 1 = 80 V I = 6 A V 2 = 120 V = 13.3 Ω = 9 A

ELECTRIC POWER The amount of work done in a given unit of time. P = V I Units: volts x amperes = J/C x C/s = J/s = watts (W) P = I 2 RP = V I The faster the transfer of charge, the more power generated in the circuit.

Example: A current of 6A flows through a resistance of 300 Ω for 1 hour. A) What is the power? I = 6 A R = 300 Ω t = 1 hour P = I 2 R = ( 6A) 2 (300Ω ) = 10,800 W b. How much heat is generated? E = Pt = 10800J/s(3600s) = 3.89x10 7 J This question asks, how many joules of electric energy are are converted into heat energy. To answer we need to remember that Power is Joules/sec, so to find the amount of energy we used, we take the power and multiply by time it runs in seconds

Example: The Elder’s keep their 40 W porch light on at night to welcome late night visitors. If the light in on from 6 pm to 7 am, and the Elder’s pay $/kwh, how much does it cost to run the light for a week? = (?kW)(?hr) ( $/kWh) 7 days x 13 hrs x = 91 hr 1 day 40 W x 1kW = kW 1000 W = (0.040 kW)(91 hr) ( $/kWh) Cost = E ($/kWh) Cost = Pt ($/kWh) = $ 0.41

RESISTORS IN SERIES To wire in SERIES means to make a circuit with a single pathway for the current.

RULES FOR RESISTORS IN SERIES - In a series circuit, the current is the same at all points along the wire. I T = I 1 = I 2 = I 3 - An equivalent resistance is the resistance of a single resistor that could replace all the resistors in a circuit. The single resistor would have the same current through it as the resistors it replaced. R E = R 1 + R 2 + R 3 - In a series circuit, the sum of the voltage drops equal the voltage drop across the entire circuit. V T = V 1 + V 2 + V 3

Example: Two resistances of 2 Ω and 4 Ω respectively are connected in series. If the source of emf maintains a constant potential difference of 12 V, a. What is the current delivered to the external circuit? R e = R 1 + R 2 = 2 Ω + 4 Ω = 6 Ω 2 A = 2 A b. What is the potential drop across each resistor? V 1 = I R 1 = 2A(2 Ω) 4 V = 4 V V 2 = I R 2 = 2A(4 Ω) 8 V = 8 V

RESISTORS IN PARALLEL To wire in PARALLEL means to make a circuit with multiple pathways for the current.

Rules for PARALLEL CIRCUITS parallel circuit total current is the sum of the currents - In a parallel circuit, each resistor provides a new path for electrons to flow. The total current is the sum of the currents through each resistor. I T = I 1 + I 2 + I 3 equivalent resistance - The equivalent resistance of a parallel circuit decreases as each new resistor is added. voltage drop - The voltage drop across each branch is equal to the voltage of the source. V T = V 1 = V 2 = V 3

Example: A 5Ω and 10Ω resistor are wired in parallel to 6V battery. A. What is their equivalent resistance? R 1 = 5Ω R 2 = 10Ω V= 6V 1= R T 5 10 R T = 3.33 Ω B. What is the current through each resistor? = 6 V 5 Ω = 1.2 A = 6 V 10 Ω = 0.6 A = 6 V 3.33Ω I T = 1.80A

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