Chapter 21 Electric Current and Direct- Current Circuits

Menu Electric Current Resistance and Ohm s Law Energy and Power in Electric Circuits Resistors in Series and Parallel

HW # 5 Pg. 754 759: # 7, 8, 11, 19, 22, 28, 32, 44, 49, 73, 78 PHYS 1402.01 Due on Monday, Oct. 7 PHYS 1402.02 Due on Tuesday, Oct. 8

Electric Current Electric current is the flow of electric charge from one place to another. A closed path through which charge can flow, returning to its starting point, is called an electric circuit.

Up to now, we have been considering equilibrium configurations of charges -- electrostatics. Now we will consider steady-state motions of charges. Electrical current I dq dt Coulomb units : second Ampere(A) By convention +I denotes the direction of positive charge flow (or the opposite direction of negative charge flow). drift velocity I nqv d A # charges/volume

Electric Current A battery uses chemical reactions to produce a potential difference between its terminals. It causes current to flow through the flashlight bulb similar to the way the person lifting the water causes the water to flow through the paddle wheel.

Example # 1 The cell membrane separates the interior of a living cell from its surroundings. Socalled ion channels penetrate the membrane, allowing passage of materials into an out of the cell. A particular channel opens for 1.0 ms and allows passage of 1.1 X 10 singly ionized potassium ions during this time. What s the current in the channel?

Example # 2 How many coulombs of charge are in one ampere-hour?

Example # 3 A steady current of 2.5 A exists in a wire for 4.0 min. (a) How much total charge passed by a given point in the circuit during those 4.0 min? ( b ) How many electrons would this be?

Electric Current A battery that is disconnected from any circuit has an electric potential difference between its terminals that is called the electromotive force or emf: Remember despite its name, the emf is an electric potential, not a force. The amount of work it takes to move a charge ΔQ from one terminal to the other is:

Electric Current The direction of current flow from the positive terminal to the negative one was decided before it was realized that electrons are negatively charged. Therefore, current flows around a circuit in the direction a positive charge would move; electrons move the other way. However, this does not matter in most circuits.

Resistance and Ohm s Law Under normal circumstances, wires present some resistance to the motion of electrons. Ohm s law relates the voltage to the current: Be careful Ohm s law is not a universal law and is only useful for certain materials (which include most metallic conductors).

Resistance and Ohm s Law Solving for the resistance, we find The units of resistance, volts per ampere, are called ohms: Resistor symbol??

Practical resistors:

Example # 4 When a potential difference of 18 V is applied to a given wire, it conducts 0.35 A of current. What is the resistance of the wire?

Resistance and Ohm s Law Two wires of the same length and diameter will have different resistances if they are made of different materials. This property of a material is called the resistivity.

Resistance and Ohm s Law The difference between insulators, semiconductors, and conductors can be clearly seen in their resistivities:

Resistance and Ohm s Law In general, the resistance of materials goes up as the temperature goes up, due to thermal effects. This property can be used in thermometers. Resistivity decreases as the temperature decreases, but there is a certain class of materials called superconductors in which the resistivity drops suddenly to zero at a finite temperature, called the critical temperature T C.

Example # 5 Nichrome is a nickel chromium alloy used in heating applications like electric toasters, because it has a relatively high resistivity and heats up when current passes through it. Suppose you have a nichrome wire 0.20 mm in diameter and 75 cm long. ( a ) What s its resistance? ( b) Find the current when a potential difference of 120 V is connected across the wire s ends.

Energy and Power in Electric Circuits When a charge moves across a potential difference, its potential energy changes: Therefore, the power it takes to do this is

Energy and Power in Electric Circuits In materials for which Ohm s law holds, the power can also be written: This power mostly becomes heat inside the resistive material.

Example # 6 (Your turn) Consider a 60 W light bulb, connected to a 120 V voltage source. What is the current passing through the wire in the bulb? (A) 0.5 A (B) 1.0 A (C) 2.0 A (D) 240 A What is the resistance of the wire in the bulb? (A) 0.5 W (B) 1.0 W (C) 2.0 W (D) 240 W

What is the current passing through the wire in the bulb? 1. 0.5 A 2. 1.0 A 3. 2.0 A 4. 240 A

What is the resistant of the wire in the bulb? 1. 0.5 A 2. 1.0 A 3. 2.0 A 4. 240 A

Conceptual Checkpoint 21-2 A battery that produces a potential difference V is connected to a 5-W lightbulb. Later the 5-W lightbult is replaced with a 10- W lightbulb. (a) In which case does the battery supply more current? 1. 5 -W 2. 10-W

Conceptual Checkpoint 21-2 A battery that produces a potential difference V is connected to a 5-W lightbulb. Later the 5-W lightbult is replaced with a 10- W lightbulb. (b) Which lightbulb has the greater resistance? 1. 5 -W 2. 10-W

Example # 7 pb. # 29 a) Find the power dissipated in a 25-Ω electric heater connected to a 120- V outlet. 1. 0.60 kw 2. 1.0 kw 3. 0.58 kw 4. 2.6 kw

Energy Use: Energy and Power in Electric Circuits When the electric company sends you a bill, your usage is quoted in kilowatt-hours (kwh). They are charging you for energy use, and kwh are a measure of energy.

Example # 8 Electric utilities measure energy in kilowatt-hours (kwh), where 1 kwh is the energy consumed if you use energy at the rate of 1 kw for 1 hour. If your monthly electric bill (30 days) is $100 and you pay 12.5c/kWh, what s your home s average power consumption and average current, assuming a 240-V potential difference between the wires supplying your home? Response for first question 1. 2.1 kw 2. 1.0 kw 3. 1.1 kw 4. 2.6 kw

Example # 9 Several male students in the same dorm room want to dry their hair. Having taken PHYS 1402 at UTPA, they have set their hair dryers to the low, 1000-W settings. Assuming a standard 120-V how many hair dryers can they operate simultaneously without tripping the 20-A circuit breaker? 1. 9.0 A 2. 8.6 A 3. 9.03 A 4. 8.33 A

Resistors in Series Resistors connected end to end are said to be in series. They can be replaced by a single equivalent resistance without changing the current in the circuit.

Example # 10 Two resistors, one having half the resistance of the other, are connected to a battery as shown on the board. What is the voltage across the bigger resistor? 1. A 2. B 3. C 4. D V b V b 3V b 2V b / 2 / 3 / 2 / 3

Example # 11 Two resistors, one having half the resistance of the other, are connected to a battery as shown on the board. What is the voltage across the bigger resistor? 1. A 2. B 3. C 4. D V b V b 3V b 2V b / 2 / 3 / 2 / 3

Resistors in Series Since the current through the series resistors must be the same in each, and the total potential difference is the sum of the potential differences across each resistor, we find that the equivalent resistance is:

Resistors in Series Since the current through the series resistors must be the same in each Total potential difference from point A to point B must be the emf of the battery ε ε = V 1 + V 2 + V 3.

Resistors in Series and Parallel Resistors are in parallel when they are across the same potential difference; they can again be replaced by a single equivalent resistance:

Resistors in Series and Parallel Using the fact that the potential difference across each resistor is the same, and the total current is the sum of the currents in each resistor, we find: Note that this equation gives you the inverse of the resistance, not the resistance itself!

Resistors in Series and Parallel If a circuit is more complex, start with combinations of resistors that are either purely in series or in parallel. Replace these with their equivalent resistances; as you go on you will be able to replace more and more of them.