1. Electric Current and Circuits

2. What is Current? Electric current is a flow of electric charge Electric current is a flow of electric charge I = Q/t I = Q/t By convention from + to – By convention from + to – Actually electrons flow away from – and toward + Actually electrons flow away from – and toward + Symbol of current is I Symbol of current is I Unit is the ampere (A) Unit is the ampere (A)

3. 1 Ampere = 1 Coulomb/Second

4. Batteries Batteries produce charge continuously from chemical reactions Batteries produce charge continuously from chemical reactions Consist of two dissimilar metals in an electrolyte (liquid, paste, or gel) Consist of two dissimilar metals in an electrolyte (liquid, paste, or gel)

5. Current is Flow of Charge in a Conductor I =  Q/  t I =  Q/  t Example: A steady current of 4.0 amperes flows in a wire for 3 minutes. How much charge passes through the wire? Example: A steady current of 4.0 amperes flows in a wire for 3 minutes. How much charge passes through the wire? 720 Coulombs

6. Charge = Current x time Q = I  t Q = I  t How many coulombs of charge will a 60 amp-hour battery deliver? How many coulombs of charge will a 60 amp-hour battery deliver? 216,000 Coulombs

7. Current Flows in an Electric Circuit A continuous conducting path is called a circuit A continuous conducting path is called a circuit Current flows through the Current flows through the wires from one terminal wires from one terminal of the battery to another of the battery to another Courtesy http://www.uce.ac.uk/education/research/cript/electricity%20book/water%20model%20electric%20circuit.htm

8. Current Must Flow in a Continuous Loop If there is a break anywhere in the loop circuit is OPEN. No current flows. If there is a break anywhere in the loop circuit is OPEN. No current flows. If no break circuit is CLOSED. Current flows. If no break circuit is CLOSED. Current flows.

9. Current Must Flow in a Continuous Loop If there is a break anywhere in the loop circuit is OPEN. No current flows. If there is a break anywhere in the loop circuit is OPEN. No current flows. If no break circuit is CLOSED. Current flows. If no break circuit is CLOSED. Current flows.

10. What Really Happens Potential difference between terminals of battery sets up an electric field in the wire and just outside parallel to it Potential difference between terminals of battery sets up an electric field in the wire and just outside parallel to it Free electrons leave negative terminal of battery, pass through circuit and re-enter battery at positive terminal Free electrons leave negative terminal of battery, pass through circuit and re-enter battery at positive terminal

11. Sponge analogy Wire is full of electrons Wire is full of electrons When you put one in, another comes out the other end When you put one in, another comes out the other end Like saturated sponge Like saturated sponge

12. Ohm’s Law Current flow is proportional to voltage Current flow is proportional to voltage Inversely proportional to resistance Inversely proportional to resistance Resistance is constant of proportionality Resistance is constant of proportionality I is current I is current V = I R V = I R I = V/R R=V/I I = V/R R=V/I

13. Ohm’s Law

14. Ohm’s Law V = IR What happens to current if you increase V? What happens to current if you increase V? What happens if you increase R? What happens if you increase R?

15. UNITS Voltage Volt (V) Voltage Volt (V) Current Amperes (A) Current Amperes (A) Resistance Ohm(  ) Resistance Ohm(  )

16. Draw a Graph of V as a function of I for a Resistor of Constant R V = IR

17. Resistance Resistance of a metal wire: Resistance of a metal wire: R =  L/A  is resistivity R =  L/A  is resistivity L is length of wire L is length of wire A is cross sectional area Silver has lowest resistivity Copper is almost as low Gold and Aluminum low too

18. Superconductivity Resistance of certain materials Resistance of certain materials becomes zero at low temperatures becomes zero at low temperatures Niobium-titanium wire at 23K Niobium-titanium wire at 23K Yttrium-Barium-Copper-Oxygen at 90K Yttrium-Barium-Copper-Oxygen at 90K Bismuth-strontium-calcium copper oxide Bismuth-strontium-calcium copper oxide Can make strong electromagnets that do not require power Can make strong electromagnets that do not require power Japanese Maglev Train goes 329 mph Japanese Maglev Train goes 329 mph

19. Power Power = Current x Voltage Power = Current x Voltage Power = energy/time = QV/time = IV Power = energy/time = QV/time = IV Unit: watt Unit: watt

20. Examples (P = IV; V = IR) What power does a 6 amp toaster operating at 120 volts use? What power does a 6 amp toaster operating at 120 volts use? What power is used by a 120 volt motor with an operating resistance of 10 ohms? What power is used by a 120 volt motor with an operating resistance of 10 ohms? What current is drawn by a 100 watt headlamp on a car (12 volt)? What is its operating resistance? What current is drawn by a 100 watt headlamp on a car (12 volt)? What is its operating resistance? 720 watts 1440 w 8.33 A; 1.44 ohms( 

21. Cost of an Electric Heater How much would it cost to operate a 1500 watt electric heater continuously for one month if the power company charges $.13 per kwh? How much would it cost to operate a 1500 watt electric heater continuously for one month if the power company charges $.13 per kwh? (b) What is the resistance of this heater (b) What is the resistance of this heater (assume V = 120V) (assume V = 120V) $140.40 9.6 ohms

22. Power IV = I 2 R = V 2 /R IV = I 2 R = V 2 /R

23. Will it Blow? A 1200 watt hair dryer, a 6 amp pump motor, and a 250 watt TV are operating on the same 20 amp circuit. How many 100 watt light bulbs could be turned on without overloading the circuit (and blowing the fuse or tripping the breaker?) A 1200 watt hair dryer, a 6 amp pump motor, and a 250 watt TV are operating on the same 20 amp circuit. How many 100 watt light bulbs could be turned on without overloading the circuit (and blowing the fuse or tripping the breaker?)

24. AC - DC DC is direct current. DC is direct current.  Steady  Comes from battery or power supply AC is alternating current AC is alternating current  Sine wave with frequency of 60 Hz (in U.S.)

25. AC

26. Electric Power Power = energy transformed/time = QV/t Power = energy transformed/time = QV/t P = IV unit: watt P = IV unit: watt Since V = IR Since V = IR P = IV = I 2 R = V 2 /R P = IV = I 2 R = V 2 /R In power transmission, why is high voltage advantageous?

27. Series Resistive Circuit Full current goes through all circuit components Full current goes through all circuit components I

28. Batteries in Series When batteries or other sources of potential are connected in series, the total potential difference is the algebraic sum of the separate potentials. When batteries or other sources of potential are connected in series, the total potential difference is the algebraic sum of the separate potentials. 6V + 6V = 12V 6V + 6V = 12V Another example: a 9 volt radio battery consists of 6 1.5 volt cells in series. Another example: a 9 volt radio battery consists of 6 1.5 volt cells in series.

29. Batteries in Parallel The voltages do not add but more current is available The voltages do not add but more current is available

30. Parallel Resistive Circuit Same voltage across all circuit elements Same voltage across all circuit elements I T = I 1 + I 2 + I 3 + I T = I 1 + I 2 + I 3 + V/R T = V/R 1 + V/R 2 + V/R 3 V/R T = V/R 1 + V/R 2 + V/R 3 1/R T = 1/R 1 + 1/R 2 + 1/R 3 + 1/R T = 1/R 1 + 1/R 2 + 1/R 3 +

31. Only Two Resistors R T = R 1 R 2 /(R 1 + R 2 ) R T = R 1 R 2 /(R 1 + R 2 ) Adding a parallel resistor reduces total resistance Adding a parallel resistor reduces total resistance

32. Summary In a series circuit there is only one current, but many voltages (across each resistance and the battery) In a series circuit there is only one current, but many voltages (across each resistance and the battery) In a parallel circuit there is only one voltage but many currents (in each of the branches) In a parallel circuit there is only one voltage but many currents (in each of the branches)

33. Solving Circuits Can have both series and parallel parts Can have both series and parallel parts Find equivalent resistances starting from point furthest away from battery Find equivalent resistances starting from point furthest away from battery Use Kirchoff’s Rules Use Kirchoff’s Rules  Voltages around a closed loop add to zero(conservation of energy)  Sum of currents entering a junction equals sum of currents leaving(conservation of charge)

34. Find all Possible Currents and Voltages Around loop voltage “drops” add up to battery voltage – use to find certain voltages by subtraction Around loop voltage “drops” add up to battery voltage – use to find certain voltages by subtraction Keep applying Ohm’s Law Keep applying Ohm’s Law At junction, currents divide up in inverse proportion to resistance they “see” At junction, currents divide up in inverse proportion to resistance they “see” If you have two loops with batteries or wires that cross you may need to apply Kirchoff’s Laws formally to obtain simultaneous equations If you have two loops with batteries or wires that cross you may need to apply Kirchoff’s Laws formally to obtain simultaneous equations

35. EMF and Terminal Voltage Battery is said to be a “seat” of electromotive force or emf Battery is said to be a “seat” of electromotive force or emf Emf is not a force Emf is not a force Real batteries have internal resistance r Real batteries have internal resistance r Terminal voltage is less than emf when internal resistance is accounted for Terminal voltage is less than emf when internal resistance is accounted for V ab = E - Ir V ab = E - Ir

36. Capacitors in Parallel Total charge is sum of charges on individual capacitors Total charge is sum of charges on individual capacitors Q = Q 1 +Q 2 + Q 3 = C 1 V +C 2 V + C 3 V Q = Q 1 +Q 2 + Q 3 = C 1 V +C 2 V + C 3 V Q = C T V Q = C T V C T V = C 1 V +C 2 V + C 3 V C T V = C 1 V +C 2 V + C 3 V C T = C 1 + C 2 + C 3 C T = C 1 + C 2 + C 3

37. Capacitors in Series Charge same on each capacitor Charge same on each capacitor Q = C T V Q = C T V V = V 1 + V 2 + V 3 V = V 1 + V 2 + V 3 Q/C T = Q/C 1 + Q/C 2 + Q/C 3 Q/C T = Q/C 1 + Q/C 2 + Q/C 3 1/C T = 1/C 1 + 1/C 2 +1/C 3 1/C T = 1/C 1 + 1/C 2 +1/C 3

38. Ammeters and Voltmeters Ammeters have low resistance and are placed in series Ammeters have low resistance and are placed in series Voltmeters have high resistance and are placed in parallel Voltmeters have high resistance and are placed in parallel Multimeter measures current, voltage and resistance Multimeter measures current, voltage and resistance