Chapter 13: Electric Circuits

1. Chapter 13: Electric Circuits Brent Royuk Phys-110 Concordia University

2. The “Minds of Our Own” Challenge • Light a bulb with a battery and a wire. Could you do it?

3. Introduction • Batteries supply charge to produce a current • How? Electrochemistry stuff: oxy/redux • cathode and anode • dry cell vs. battery • Electric current = moving charges • dc vs. ac • How does this relate to electrostatics? • Electroscope and D-cell? • Voltage of charge strips • Current Flow • Consider a simple circuit diagram • What direction does the current flow? • Electron flow vs. conventional current • Curse you Ben Franklin!

4. Electric Current • Definition: • Unit: The ampere (A) • “amps” • 1 A = 6.25 x 1018 electrons/s • What about AC current? • What makes current flow? A voltage, or EMF. • EMF=electromotive force

5. The Water Pump Analogy

6. Drift Velocity • Even without a potential, electrons are in constant motion • Electric field --> force --> drift velocity • How many conduction electrons are in a wire? • So drift velocities are often very slow, like walking speeds. • So why don’t we have to wait for the light when we hit the switch? • What moves fast? • “Marbles in a tube” analogy

7. Ohm’s Law • Two laws for resistive circuits: • I V • I 1/R • Put them together and you get V = IR • Ohm’s Law • Definition of resistance: R = V/I • Resistance Unit: The ohm () • Ohm’s Law doesn’t apply to all materials • E.g. semi-conductors, lightbulb filaments • Ohmic vs. non-ohmic materials

8. Resistivity • Resistivity is a measure of how well a material conducts electricity. • Resistance also depends on the material dimensions of the conductor. • Further define conductivity as

9. Table of Resistivities How about a real copper wire?

10. Superconductors • Type 1 • Pb, Hg, Sn, Cr, Al • For Pb, Tc = 7.2 K • Type 2 • 1986: Superconducting oxocuprates • Tc > 100K

11. Series vs. Parallel

12. Resistors in Series & Parallel • Series • Voltage drops across the resistors in a series circuit • So V = V1 + V2 + V3 +... • Therefore, • Parallel • Current is conserved in a parallel circuit. • So I = I1 + I2 + I3 +... • Therefore,

13. Examples • Connect two resistors of resistance R in series and parallel. What is the equivalent resistance? • Expression for R1 and R2 in parallel. • Three 150-ohm resistors are connected in parallel with a 12-V battery. What is the total power dissipation? • Connect two bulbs in series and parallel. Which pair is brighter? • Bulb board

14. Combination Circuits • Use the method of circuit reduction to reduce complex circuits into simpler ones. • Assume a 10-V potential source and 10-ohm resistors below. Fill in the meters. • Voltmeters vs. ammeters • Voltmeters: Parallel, high resistance • Ammeters: Series, low resistance

15. Electric Power • A charge moving through a circuit expends energy • This is due to collisions between electrons and resistor molecules. • Voltage drops across a resistor • U = VQ, so divide by time. • P = VI • A standard flashlight bulb is rated at 5.2 V, 850 mA. What is its wattage? • Combining with Ohm’s Law, we get

16. Joule Heating • Energy that heats a resistor is sometimes called the Joule heat • That’s how electric heaters, hair dryers, etc. work • Sometimes this is bad, as in e.g. energy loss in power lines • P = I2R, so should heaters have high resistance or low resistance? • Try This Box 13.4: A 60-W light bulb is designed to operate on 120 V ac. What is the current drawn by the bulb? What is the resistance of the filament?

17. Energy Bills • What is a kilowatt-hour (kWh)? • How much does it cost to light a 100-W bulb for a month?

18. Home Electricity • Three-wire system: difference between two hot is 240 V, most appliances connect between one hot and a ground wire for a difference of 120 V • Demo with hot wire, voltmeter • Appliances are wired in parallel: Why?

19. Home Electricity

20. Electric Safety Two problems to prevent: • Too much current can flow in a circuit, causing Joule heating of the circuit, possibly starting fires. • Solution: Fuses & circuit breakers • Electricity can electrocute people. • Solution: Three prong plugs, polarized plugs, fuses & circuit breakers

21. Limiting Current in Circuits • Fuses and Circuit Breakers

22. Electric Safety • Problem: disconnected wire can make appliances “hot” • Demo grounding plug: polarized plug vs. dedicated grounding wire. • adapters have grounding lugs • Path through body is important; hand vs. chest • Why isn’t a car battery dangerous?

23. Electric Safety • Three Conditions for Danger • Enough Voltage to Cause Current • Enough Charge/Current to Cause Damage • Electrical Path Through Body

24. Human Resistance Resistance is Futile 1999 Darwin Award Nominee (1999) A US Navy safety publication describes injuries incurred while doing don'ts. One page described the fate of a sailor playing with a multimeter in an unauthorized manner. He was curious about the resistance level of the human body. He had a Simpson 260 multimeter, a small unit powered by a 9-volt battery. That may not seem powerful enough to be dangerous… but it can be deadly in the wrong hands. The sailor took a probe in each hand to measure his bodily resistance from thumb to thumb. But the probes had sharp tips, and in his excitement he pressed his thumbs hard enough against the probes to break the skin. Once the salty conducting fluid known as blood was available, the current from the multimeter traveled right across the sailor's heart, disrupting the electrical regulation of his heartbeat. He died before he could record his Ohms. The lesson? The Navy issues very few objects which are designed to be stuck into the human body.

25. Electric Safety • Effects of Electric Current on the Human Body • Current (approximate) Effect • 0–0.5 mA none • 0.5–2 mA Threshold of feeling • 2–10 mA Pain; muscular contractions. • 10–20 mA Increased muscular effect, some injury; above 16 mA is the'let-go' current above which a person cannot release held objects. • 20–100 mA Respiratory paralysis • 100 mA–3 A Ventricular fibrillation; fatal unless resuscitation occurs immediately. • above 3 A Cardiac arrest; heart can be restarted if shock is very brief; severe burns

26. Electric Safety • Electrical resistance of a dry body: 100,000  • Electrical resistance of a wet body: 1500  An electrical model of the human body is a leather bag filled with salt water. The resistance of the skin (leather) can be high when dry, but drops by orders of magnitude when it get wet. Ions in the skin go into solution. Below the skin the resistance is very low (blood, organs etc). If the skin is breached, a voltage well below 100 volts can produce lethal currents. Some people survive brushes with very high voltages (like 100kV) because they draw an arc inches before they actually touch the conductor. With luck the muscular contractions push the victim away from the danger rather then into it.

27. The Resistor Code

28. The Resistor Code • B   B   ROY   of   Great   Britain   had a   Very   Good   Wife • Bad Betty runs over your garden but Violet Gray won't • Big boys race our young girls, but violet generally wins • Black Beetles Running On Your Garden Bring Very Good Weather • Big Bears Run Over Your Gladiola Bed Vexing Garden Worms (go see now) • Beer Bottles, Reminders Of Your Guests, Become Voluminous Glass Waste • Behold Brother, Rain On Your Grapes Brings Very Good Wine • Bad Booze Rots Our Young Guts, But Vodka Goes Well