Electric Current and Resistance

1. Electric Current and Resistance Chapter 17

2. Batteries • Batteries create a difference in potential [J/C] between two leads called the anode and the cathode. • Anode and cathode are different types of metal which react with the electrolyte (solution) inside the battery. • Anode is the positive side and cathode is the negative side. • Chemical energy transforms to electrical energy.

3. Batteries • The battery is capable of maintaining a difference in potential energy. • Any device that can maintain a potential difference is called a power supply. • Batteries create DC (direct current) because charge flows in one direction.

4. Terminal Voltage vs. Emf • Emf stands for electromotive force but it is NOT a force but a voltage! • Emf gives the potential difference across a battery when nothing is connected (no current flows) – this is a maximum voltage • When current flows through the battery, the battery provides some internal resistance that slightly reduces this Emf • Terminal voltage is the ‘operating voltage’ of a battery. • Normally Emf and terminal voltage are essentially the same. • V = Emf - IR

5. Emf • A ‘non-ideal’ battery has a large internal resistance.

6. Circuit Symbols • Learn the basic symbols for creating electric circuits! • A circuit is a complete loop through which current can flow.

7. Practice • Use the appropriate symbols to sketch a complete circuit containing two 6 V batteries in series wired to two identical capacitors in parallel, followed by two resisters in series.

8. Current • Static electricity (chapters 15, 16) refers to charges that are not moving. • Electric current refers to charges that flow. • Electric current tells how much charge flows per second • I = q/t [Coulomb/sec] = [Ampere] = [A]

9. Current • Electric current give the charge flowing past a particular area per second. • Though it is electrons that actually flow, current is defined as the flow of positive charge.

10. Example • Suppose there is a steady current of 0.50 A in a flashlight bulb lasting for 2.0 minutes. How much charge passes through the bulb in this time? How many electrons does this represent?

11. Drift Velocity • Electrons in a wire don’t ‘flow’ in the same manner as water in a pipe. • In the absence of a potential difference, V, the electrons in a conductor move randomly at high speeds, making many collisions with atoms. • When a potential difference is applied, this random motion changes: electrons begin to drift in the direction of the voltage.

12. Drift Velocity • Electrons move opposite the direction of the electric field. • When voltage is applied, their random motion becomes slightly less random…

13. Homework • # 10 - 13, 21 - 24 page 586 • Also # 1 – 7, 15 - 19 if not already done

14. Resistance and Ohm’s Law • Current flows less easily through thinner wires than through thicker wires. • Materials that resist the flow of electric current are caller resistors. • Resistance is the opposition to the flow of electricity. • For a given voltage difference, current will be smaller if the resistance of a material is higher. • R = V/I

15. Resistance and Ohm’s Law • R = V/I [Volt/Amp] = [Ohm] = [Ω] • V = IR is Ohm’s Law • If you know the total resistance in a circuit powered by a particular voltage, you can find the current.

16. Example • Any room in the house that is exposed to water and electrical voltage can present hazards. For example, suppose a person steps out of a shower and inadvertently touches an exposed 120 V wire (frayed end of the hairdryer) with a wet finger. When wet, the human body has a resistance of only 300Ω. Find the current in the person’s body.

17. Factors Influencing Resistance • Resistance is inversely proportional to the cross sectional area of a wire and directly proportional to length: • R = ρ L/A where ρ is the materials resistivity

18. Resistivity • The resistivity, ρ, of a material may increase with temperature. • ρ=ρ0(1+αΔT) where α = temperature coefficient of resistivity • R = R0(1+αΔT)

19. Resistivities

20. Example • A platinum wire has a resistance of 0.5 Ω at zero degrees Celsius. It is placed in a water bath where its resistance rises to 0.6 Ω. Find the temperature of the water bath.

21. Superconductivity • Resistance increases as temperature increases. • Therefore resistance decreases as temperature decreases… • Superconductivity occurs when the resistance is exactly zero. • Temperatures near 100K produce superconductivity (very difficult to achieve outside of a lab environment)

22. Electric Power • Power = Work/time = V·q/t = V·I = [J/C][C/s] [Watt] • P = VI • The power provided by a battery as it pushes charge through a potential difference P = VI. • This formula is valid as long as voltage and current are constant over time.

23. Power • Power is also used (dissipated) by each resistor in the circuit (resistors turn energy into heat) • P = VI = (IR)I = I2R • P = VI = V(V/R) = V2/R

24. Example • Consider two appliances that operate at the same voltage. Appliance A has a higher power rating than Appliance B. a) How does the resistance of A compare with the resistance of B?

25. Example • A computer system includes a monitor with a power requirement of 200 W, whereas a countertop broiler/ toaster oven is rated at 1500 W. Calculate the resistance of each if they are designed to run at 120 V?

26. Summary • V = IR Ohm’s Law • P = VI Power • P = I2R = V2/R • If power rating is higher, resistance is lower for appliances operating at the same voltage.

27. Homework • Read Examples 17.7 and 17.8 on pages 582 – 582 • Do # 27 – 29, 36, 38, 42, 44, 48, 52, 62, 63, 66, 68, 72, 73, 78, 79 Chapter 17.