February 4 th , 2013 Current, voltage, resistance, DC circuits

1. Chapter 19 February 4th, 2013 Current, voltage, resistance, DC circuits

2. Electric Circuits • A circuit occurs when charge can flow in a closed path • Circuit components: • Resistors (Ohm’s Law V=IR) • Capacitors (I(t), V(t), Q(t)) • Conservation principles and Kirchhoff’s rules

3. Electric Current • Current, I, is defined as the net positive charge flow • However, only e- move • Units: Ampere (A) • In honor of André-Marie Ampère (French, 1775-1836) • 1 A = 1 C / s

4. Movement of Charges • The definition of current uses the net charge, Δq, that passes a particular point during a time interval, Δt • The amount of charge could be the result of many possible configurations, including • A few particles each with a large charge • Many particles each with a small charge • A combination of positive and negative charges • In wires, only e- move, and they move slowly -1 cm/sec • but the light comes on as soon as you flip the switch

5. Current and Potential Energy • For charge to move along a wire, the electric potential energy at one end of the wire must be higher than at the other end • The voltage is related to the electric potential energy by PEelec= qV

6. Current and Voltage • The current is directed from higher to lower voltage • The direction of I is always from high to low potential, in both cases: • if the current is carried by positive or negative charges • The potential difference may be supplied by a battery

7. Construction of a Battery • Alessandro Volta (Italian, 1745-1827) developed the first batteries • Batteries convert chemical energy into electrical energy • In drawing an electric circuit the terminals of any type of battery are labeled with + and - copper cathode (+) very cool chemistry! zinc anode (-)

8. Volta’s Batteries • Volta’s first batteries consisted of alternating sheets of zinc and copper • They were separated by a piece of parchment (animal skin) soaked in salt water

9. EMF (or….how to get a bad reputation for physics!) emf=V=DV=potential=potential difference • In order to torture you, the potential difference between a battery’s terminals is called electromotive force, or emf • Emf is NOT A FORCE! The term was adopted before it was understood that batteries produce an electric potential difference, not a force • The emf is denoted with ε and referred to as voltage • The value of εdepends on the particular chemical reactions the battery employs and how the electrodes are arranged

10. Simple Circuit • If the battery terminals are connected by a wire, a current is produced • The electrons move out of the negative terminal of the battery through the wire and into the positive battery terminal • The electrons move through the wire – to +, and the battery slowly runs down. the chemistry inside the battery can’t keep up the same pace.

11. Ideal vs. Real Batteries • An ideal battery: • always maintains a fixed voltage between its terminals • This voltage is maintained no matter how much current flows from the battery • Real batteries have two practical limitations: • The emf decreases when the current is very high • The electrochemical reactions do not happen instantaneously • The battery will “run down” • It will not work forever

12. A pacemaker requires 0.50 µA of continuous current. If a Lithium-iodine battery is capable of supplying 0.50 Ah of charge, what is the lifetime of the battery? Does this lifetime seem sufficiently long? Problem 19.7

13. Current • The electrons moving in a wire collide frequently with one another and with the atoms of the wirezigzag motion • When no voltage is applied, the average displacement is zero • With a battery connected, there is an electric field • The electric field produces a force that gives the electrons a net motion • The velocity of this motion is the drift velocity (-1 cm/s)

14. demo Board with pegs: ball bearing fall is delayed by many collisions, analogous to electrons in wires • In wires, e- move slowly -1 cm/sec • but the light comes on as soon as you flip the switch

15. Ohm’s Law • The greater the voltage, the greater the electric field, thus the greater the drift velocity. • The current is proportional to the drift velocity, so the current is proportional to the voltage I α V

16. Ohm’s Law, cont. • The constant of proportionality between I and V is the electrical resistance, R • This relationship is called Ohm’s Law (Pupa calls it the manly law, or the VIRile law) • The unit of resistance is an Ohm, Ω • 1 Ω= 1 Volt / Ampere • The resistance of a wire depends on its composition, size, and shape

17. Question R1=1W V0 R10=10W Compare V1 the voltage across R1with V10 the voltage across R10 V1<V10 V1=V10 V1>V10 V = I R V1 = I1 R1 = I V10 = I10 R10 = 10 I

18. Question R1=1W V0 R10=10W Compare I1 the current through R1 and I10 the current through R10 I1<I10 I1=I10 I1>I10 The current remains constant throughout the circuit--because there is no where else for the current to go I = V/R I1= V1/R1 I10= V10/R10= 10V1/10R1 = I1

19. Resistivity • The resistivity, ρ, depends only on the material used to make the wire • The resistance of a wire of length L and cross-sectional area A is given by

20. Ohm’s Law: Final Notes • Ohm’s Law predicts a linear relationship between current and voltage • Ohm’s Law is not a fundamental law of nature • Many, but not all, materials and devices obey Ohm’s Law • Resistors do obey Ohm’s Law • Resistors will be used as the basis of circuit ideas

21. demos Light bulb in series with coil resistor in liquid nitrogen Ohm’s Law demo

22. demo Variable resistor in series with light bulb If L increases, then R increases If R increases and V stays the same, I must decrease, thus the light bulb gets dimmer

23. Circuit Schematic • 1 resistor and 1 battery • Since the resistance of the wires is much smaller than that of the resistors, a good approximation is Rwire=0

24. Circuit Symbols

25. DC Circuits • An electric circuit is a combination of connected elements forming a complete path through which charge is able to move • Calculating the current in the circuit is called circuit analysis • DC stands for direct current • The current is constant over time • The current can be viewed as the motion of the positive charges traveling through the circuit • The current is the same at all points in the circuit

26. Circuits, cont. Current I > 0 • There must be a complete circuit for charge to flow • There must be a return path for the current to return to the voltage source • If the circuit is open, there is no current flow anywhere in the circuit Current I > 0

27. Kirchhoff’s Loop Rule • Consider the electric potential energy of a test positive charge moving through the circuit • ΔV = ε – I R = 0 • Kirchhoff’s Loop Rule: The total change in electric potential ΔV around any closed circuit loop must be zero (conservation of energy) • Since PEelec = q V, the loop rule also means the change in the PEelec around the loop is zero

28. Power • In the resistor, the energy decreases by q V = (I Δt) V • P = I V (power P is energy/Dt) • From Ohm’s Law P = I V = I² R = V² / R • The circuit converts chemical energy from the battery to heat energy in the resistors • Applies to all circuit elements

29. Resistors in Series – Equivalent R • Resistors in series will be equivalent to a single resistor with Requiv = R1 + R2 + R3 + … • An equivalent resistor means that an arrangement of resistors can be replaced by the equivalent resistance with no change in the current in the rest of the circuit • The idea of equivalence will apply to many other types of circuit elements

30. demo: 1 resistor, 3 resistors in series

31. Batteries in Series • Batteries can also be connected in series • The positive terminal of one battery would be connected to the negative terminal of the next battery • The combination of two batteries in series is equivalent to a single battery with emf of

32. Kirchhoff’s Junction Rule • The amount of current entering a junction must be equal to the current leaving it (conservation of charge) • This is called Kirchhoff’s junction rule • It is just another way of saying that charge cannot be created or destroyed • Both of Kirchhoff’s Rules may be needed to solve a circuit, that is, to find currents.

33. Resistors in Parallel • In some circuits, the current can take multiple paths • The different paths are called branches • The arrangement of resistors shown is called resistors in parallel • The currents in each branch need not be equal

34. Parallel Resistors – Equivalent R • A set of resistors in parallel can be replaced with an equivalent resistor demo: 1 resistor, 2 and 3 resistors in parallel

35. demo: 1 resistor, 3 resistors in parallel

36. Resistors Summary Ohm’s Law: V =IR if there are many resistors in series, power is mostly dissipated by the resistor with largest resistance (e.g. light bulb filament) Resistance: R = rL/A Power Dissipated: P = IV = I2R Series Parallel R1 R1 R2 R2 Voltage Differentfor each resistor. Vtotal = V1 + V2 Samefor each resistor. Vtotal = V1 = V2 Current Same for each resistor Itotal = I1 = I2 Different for each resistor Itotal = I1 + I2 Resistance Increases Req = R1 + R2 Decreases 1/Req = 1/R1 + 1/R2