Current and Resistance A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007

Objectives: After completing this module, you should be able to: Define electric current and electromotive force.Define electric current and electromotive force. Write and apply Ohm’s law to circuits containing resistance and emf.Write and apply Ohm’s law to circuits containing resistance and emf.

Electric Current Electric current I is the rate of the flow of charge Q through a cross-section A in a unit of time t. One ampere A is charge flowing at the rate of one coulomb per second. A + - Wire +Q t

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 = 6 A q = (6 A)(3 s) = 18 C Recall that: 1 e - = 1.6 x C, then convert: In 3 s: 1.12 x electrons

Conventional Current Imagine a charged capacitor with Q = CV that is allowed to discharge. Electron flow: The direction of e - flowing from – to +. Conventional current: The motion of +q from + to – has same effect. Electric fields and potential are defined in terms of +q, so we will assume conventional current (even if electron flow may be the actual flow) Electron flow +-+- e-e- Conventional flow +

Electromotive Force A source of electromotive force (emf) is a device that uses chemical, mechanical or other energy to provide the potential difference necessary for electric current. Power lines Battery Wind generator

Water Analogy to EMF Low pressure PumpWater High pressure Valve Water Flow Constriction Source of EMF Resistor High potential Low potential Switch R I +- The source of emf (pump) provides the voltage (pressure) to force electrons (water) through electric resistance (narrow constriction).

Electrical Circuit Symbols Electrical circuits often contain one or more resistors grouped together and attached to an energy source, such as a battery. The following symbols are often used: Ground Battery - + Resistor

What is a Resistor? a component of an circuit that resists the flow of electrical current.a component of an circuit that resists the flow of electrical current. It is designed to drop the voltage of the current as it flows from one terminal to the other.It is designed to drop the voltage of the current as it flows from one terminal to the other. Resistors are primarily used to create and maintain known safe currents within electrical components.Resistors are primarily used to create and maintain known safe currents within electrical components.

What is a Resistor? Resistance is measured in ohms, after Ohm's law.Resistance is measured in ohms, after Ohm's law. A high ohm rating indicates a high resistance to current.A high ohm rating indicates a high resistance to current.

Electric Resistance Suppose we apply a constant potential difference of 4 V to the ends of geometrically similar rods of, say: steel, copper, and glass. 4 V SteelCopperGlass IsIs IcIc IgIg The current in glass is much less than for steel or iron, suggesting a property of materials called electrical resistance R.

Ohm’s Law Ohm’s law states that the current I through a given conductor is directly proportional to the potential difference V between its end points. Ohm’s law allows us to define resistance R and to write the following forms of the law:

Example 2. When a 3-V battery is connected to a light, a current of.006 A is observed. What is the resistance of the light filament? Source of EMF R I +- V = 3 V 6 mA R = 500 R = 500  The SI unit for electrical resistance is the ohm, The SI unit for electrical resistance is the ohm, 

Ammeter Voltmeter Rheostat Source of EMF Rheostat A Laboratory Circuit Symbols V Emf - +

Factors Affecting Resistance 1. The length L of the material. Longer materials have greater resistance. 1 1 L 2 2 2L 2. The cross-sectional area A of the material. Larger areas offer LESS resistance. 2 2 A 1 1 2A

Factors Affecting R (Cont.) 3. The temperature T of the material. The higher temperatures usually result in higher resistances. 4. The kind of material. Iron has more electrical resistance than a geometrically similar copper conductor. RoRoRoRo R > R o R i > R c CopperIron

Electric Power Electric power is the amount of electric energy that flows through a circuit in a given amount of time.Electric power is the amount of electric energy that flows through a circuit in a given amount of time. Electric power is measured in units called watts.Electric power is measured in units called watts.

Electric Power Electric power P is the rate at which electric energy is expended, or work per unit of time. Vq V To charge C: Work = qV Substitute q = It, then: P = VI I Power = voltage x current (amps)

Calculating Power Using Ohm’s law, we can find electric power from any two of the following parameters: current I, voltage V, and resistance R. Ohm’s law: V = IR

A hair dryer needs 10 amperes of current in a 120 volt circuit. How much power does it use? Power = voltage x current 120 volts x 10 amps = 1,200 watts The hair dryer uses 1,200 watts of power every hour. A kilowatt is used to measure large amounts of electrical power. A kilowatt is equal to 1,000 watts, so the hair dryer uses 1,200 watts or 1.2 kilowatts of power.

Example 5. A power tool is rated at 9 A when used with a circuit that provides 120-V. What power is used in operating this tool? P = VI = (120 V)(9 A) P = 1080 W Example 6. A 500-W heater draws a current of 10 A. What is the resistance? R = 5.00 

Summary of Formulas Electric current: Ohm’s Law

Summary (Cont.) Electric Power P:

Direct Current Circuits A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007

Resistances in Series Resistors are said to be connected in series when there is a single path for the current. The current I is the same for each resistor R 1, R 2 and R 3. The energy gained through E is lost through R 1, R 2 and R 3. The same is true for voltages: For series connections: I = I 1 = I 2 = I 3 V T = V 1 + V 2 + V 3 R1R1 I VTVT R2R2 R3R3 Only one current

Equivalent Resistance: Series The equivalent resistance R e of a number of resistors connected in series is equal to the sum of the individual resistances. V T = V 1 + V 2 + V 3 ; (V = IR) I T R e = I 1 R 1 + I 2 R 2 + I 3 R 3 But... I T = I 1 = I 2 = I 3 R e = R 1 + R 2 + R 3 R1R1 I VTVT R2R2 R3R3 Equivalent Resistance

Example 1: Find the equivalent resistance R e. What is the current I in the circuit? 2  12 V 1  3  R e = R 1 + R 2 + R 3 R e = 3  + 2  + 1   = 6  Equivalent R e = 6  The current is found from Ohm’s law: V = IR e I = 2 A

Example 1 (Cont.): Show that the voltage drops across the three resistors totals the 12-V emf. 2  12 V 1 1  3  R e = 6  I = 2 A V 1 = IR 1 ; V 2 = IR 2; V 3 = IR 3 Current I = 2 A same in each R. V 1 = (2 A)(1 V 1 = (2 A)(1  = 2 V V 1 = (2 A)(2 V 1 = (2 A)(2  = 4 V V 1 = (2 A)(3 V 1 = (2 A)(3  = 6 V V 1 + V 2 + V 3 = V T 2 V + 4 V + 6 V = 12 V Check !

Parallel Connections Resistors are said to be connected in parallel when there is more than one path for current. 2  4 4  6  Series Connection: For Series Resistors: I 2 = I 4 = I 6 = I T V 2 + V 4 + V 6 = V T Parallel Connection: 6  2 2  4  For Parallel Resistors: V 2 = V 4 = V 6 = V T I 2 + I 4 + I 6 = I T

Equivalent Resistance: Parallel V T = V 1 = V 2 = V 3 I T = I 1 + I 2 + I 3 Ohm’s law: The equivalent resistance for Parallel resistors: Parallel Connection: R3R3 R2R2 VTVT R1R1

Example 3. Find the equivalent resistance R e for the three resistors below. R3R3 R2R2 VTVT R1R1 2  4  6  R e = 1.09  For parallel resistors, R e is less than the least R i.

Example 3 (Cont.): Show that the current leaving the source I T is the sum of the currents through the resistors R 1, R 2, and R 3. R3R3 R2R2 12 V R1R1 2  4  6  VTVT I T = 11 A; R e = 1.09  V 1 = V 2 = V 3 = 12 V I T = I 1 + I 2 + I 3 6 A + 3 A + 2 A = 11 A Check !

Short Cut: Two Parallel Resistors The equivalent resistance R e for two parallel resistors is the product divided by the sum. R e = 2  Example: R2R2 VTVT R1R1 6  3 

Series and Parallel Combinations In complex circuits resistors are often connected in both series and parallel. VTVT R2R2 R3R3 R1R1 In such cases, it’s best to use rules for series and parallel resistances to reduce the circuit to a simple circuit containing one source of emf and one equivalent resistance. VTVT ReRe

Example 4. Find the equivalent resistance for the circuit drawn below (assume V T = 12 V). R e = 4  + 2  R e = 6  VTVT 3  6  4  12 V 2  4  6  12 V

Example 3 (Cont.) Find the total current I T. VTVT 3  6  4  12 V 2  4  6  12 V ITIT R e = 6  I T = 2.00 A

Example 3 (Cont.) Find the currents and the voltages across each resistor  I 4 = I T = 2 A V 4 = (2 A)(4  ) = 8 V The remainder of the voltage: (12 V – 8 V = 4 V) drops across EACH of the parallel resistors. V 3 = V 6 = 4 V This can also be found from V 3,6 = I 3,6 R 3,6 = (2 A)(2  ) VTVT 3  6  4  (Continued...)

Example 3 (Cont.) Find the currents and voltages across each resistor  V 6 = V 3 = 4 V V 4 = 8 V VTVT 3  6  4  I 3 = 1.33 A I 6 = A I 4 = 2 A Note that the junction rule is satisfied: I T = I 4 = I 3 + I 6  I (enter) =  I (leaving)

Summary of Formulas Electric current: Ohm’s Law

Summary (Cont.) Electric Power P:

Summary of Formulas: Resistance Rule: R e =  R Voltage Rule:  E =  IR Rules for a simple, single loop circuit containing a source of emf and resistors. 2  3 V V A C B D 3  Single Loop

Summary (Cont.) For resistors connected in series: R e = R 1 + R 2 + R 3 For series connections: I = I 1 = I 2 = I 3 V T = V 1 + V 2 + V 3 R e =  R 2  12 V 1  3 

Summary (Cont.) Resistors connected in parallel: For parallel connections: V = V 1 = V 2 = V 3 I T = I 1 + I 2 + I 3 R3R3 R2R2 12 V R1R1 2  4  6  VTVT Parallel Connection