ELECTRIC CURRENTS D R M A R T A S T A S I A K D E P A R T M E N T O F C Y T O B I O L O G Y A N D P R O T E O M I C S lecture based on 2016 Pearson Education, Ltd.
The Electric Battery Electric Current Ohm s Law: Resistance and Resistors Resistivity Electric Power Power in Household Circuits Alternating Current Microscopic View of Electric Current Superconductivity Electrical Conduction in the Human Nervous System
THE ELECTRIC BATTERY Volta discovered that electricity could be created if dissimilar metals were connected by a conductive solution called an electrolyte. This is a simple electric cell.
THE ELECTRIC BATTERY A battery transforms chemical energy into electrical energy. Chemical reactions within the cell create a potential difference between the terminals by slowly dissolving them. This potential difference can be maintained even if a current is kept flowing, until one or the other terminal is completely dissolved.
THE ELECTRIC BATTERY Several cells connected together make a battery, although now we refer to a single cell as a battery as well.
ELECTRIC CURRENT is the rate of flow of charge through a conductor: Unit of electric current: the ampere, A. 1 A = 1 C/s
ELECTRIC CURRENT A complete circuit is one where current can flow all the way around. Note that the schematic drawing doesn t look much like the physical circuit!
ELECTRIC CURRENT In order for current to flow, there must be a path from one battery terminal, through the circuit, and back to the other battery terminal. Only one of these circuits will work:
ELECTRIC CURRENT By convention, current is defined as flowing from + to. Electrons actually flow in the opposite direction, but not all currents consist of electrons.
OHM S LAW: RESISTANCE AND RESISTORS Experimentally, it is found that the current in a wire is proportional to the potential difference between its ends: I V
OHM S LAW: RESISTANCE AND RESISTORS The ratio of voltage to current is called the resistance:
OHM S LAW: RESISTANCE AND RESISTORS In many conductors, the resistance is independent of the voltage; this relationship is called Ohm s law. Materials that do not follow Ohm s law are called nonohmic. Unit of resistance: the ohm, Ω. 1 Ω = 1 V/A
OHM S LAW: RESISTANCE AND RESISTORS Standard resistors are manufactured for use in electric circuits; they are color-coded to indicate their value and precision.
OHM S LAW: RESISTANCE AND RESISTORS
OHM S LAW: RESISTANCE AND RESISTORS Some clarifications: Batteries maintain a (nearly) constant potential difference; the current varies. Resistance is a property of a material or device. Current is not a vector but it does have a direction. Current and charge do not get used up. Whatever charge goes in one end of a circuit comes out the other end.
RESISTIVITY The resistance of a wire is directly proportional to its length and inversely proportional to its crosssectional area: The constant ρ, the resistivity, is characteristic of the material.
RESISTIVITY
RESISTIVITY For any given material, the resistivity increases with temperature: Semiconductors are complex materials, and may have resistivities that decrease with temperature.
ELECTRIC POWER Power, as in kinematics, is the energy transformed by a device per unit time:
ELECTRIC POWER The unit of power is the watt, W. For ohmic devices, we can make the substitutions:
ELECTRIC POWER What you pay for on your electric bill is not power, but energy the power consumption multiplied by the time. We have been measuring energy in joules, but the electric company measures it in kilowatt-hours, kwh. One kwh = (1000 W)(3600 s) = 3.60 x 10 6 J
POWER IN HOUSEHOLD CIRCUITS The wires used in homes to carry electricity have very low resistance. However, if the current is high enough, the power will increase and the wires can become hot enough to start a fire. To avoid this, we use fuses or circuit breakers, which disconnect when the current goes above a predetermined value.
POWER IN HOUSEHOLD CIRCUITS Fuses are one-use items if they blow, the fuse is destroyed and must be replaced.
POWER IN HOUSEHOLD CIRCUITS Circuit breakers, which are now much more common in homes than they once were, are switches that will open if the current is too high; they can then be reset.
ALTERNATING CURRENT Current from a battery flows steadily in one direction (direct current, DC). Current from a power plant varies sinusoidally (alternating current, AC).
ALTERNATING CURRENT The voltage varies sinusoidally with time: as does the current:
ALTERNATING CURRENT Multiplying the current and the voltage gives the power:
ALTERNATING CURRENT Usually we are interested in the average power:
ALTERNATING CURRENT The current and voltage both have average values of zero, so we square them, take the average, then take the square root, yielding the root mean square (rms) value.
MICROSCOPIC VIEW OF ELECTRIC CURRENT Electrons in a conductor have large, random speeds just due to their temperature. When a potential difference is applied, the electrons also acquire an average drift velocity, which is generally considerably smaller than the thermal velocity.
MICROSCOPIC VIEW OF ELECTRIC CURRENT This drift speed is related to the current in the wire, and also to the number of electrons per unit volume.
SUPERCONDUCTIVITY In general, resistivity decreases as temperature decreases. Some materials, however, have resistivity that falls abruptly to zero at a very low temperature, called the critical temperature, TC.
SUPERCONDUCTIVITY Experiments have shown that currents, once started, can flow through these materials for years without decreasing even without a potential difference. Critical temperatures are low; for many years no material was found to be superconducting above 23 K. More recently, novel materials have been found to be superconducting below 90 K, critical temperatures as high as 160K have been reported.
ELECTRICAL CONDUCTION IN THE HUMAN NERVOUS SYSTEM The human nervous system depends on the flow of electric charge. The basic elements of the nervous system are cells called neurons. Neurons have a main cell body, small attachments called dendrites, and a long tail called the axon.
ELECTRICAL CONDUCTION IN THE HUMAN NERVOUS SYSTEM Signals are received by the dendrites, propagated along the axon, and transmitted through a connection called a synapse.
ELECTRICAL CONDUCTION IN THE HUMAN NERVOUS SYSTEM This process depends on there being a dipole layer of charge on the cell membrane, and different concentrations of ions inside and outside the cell.
ELECTRICAL CONDUCTION IN THE HUMAN NERVOUS SYSTEM This applies to most cells in the body. Neurons can respond to a stimulus and conduct an electrical signal. This signal is in the form of an action potential.
ELECTRICAL CONDUCTION IN THE HUMAN NERVOUS SYSTEM The action potential propagates along the axon membrane.
SUMMARY A battery is a source of constant potential difference. Electric current is the rate of flow of electric charge. Conventional current is in the direction that positive charge would flow. Resistance is the ratio of voltage to current: Ohmic materials have constant resistance, independent of voltage. Resistance is determined by shape and material: ρ is the resistivity. Power in an electric circuit:
SUMMARY Direct current is constant Alternating current varies sinusoidally The average (rms) current and voltage: The average (rms) current and voltage:
EXAMPLE ELECTRIC FIELDS AROUND CHARGES
ELECTRIC FIELDS IN CIRCUITS Point away from positive terminal, towards negative Channeled by conductor (wire) Electrons flow opposite field lines (neg. charge) E electrons & direction of motion E E Electric field direction E
ELECTRON BEAMS; CATHODE RAY TUBES (CRTS) Televisions, Oscilloscopes, Monitors, etc. use an electron beam steered by electric fields to light up the (phosphorescent) screen at specified points screen cathode emitter + + + + + + + electron beam - - - - - - - E-field metal plates
DC CIRCUITS D R M A R T A S T A S I A K D E P A R T M E N T O F C Y T O B I O L O G Y A N D P R O T E O M I C S
CONTENTS EMF and Terminal Voltage Resistors in Series and in Parallel Kirchhoff s Rules EMFs in Series and in Parallel; Charging a Battery Circuits Containing Capacitors in Series and in Parallel RC Circuits Resistor and Capacitor in Series Electric Hazards Ammeters and Voltmeters Measurement Affects the Quantity Being Measured
EMF AND TERMINAL VOLTAGE Electric circuit needs battery or generator to produce current these are called sources of emf. Battery is a nearly constant voltage source, but does have a small internal resistance, which reduces the actual voltage from the ideal emf:
EMF AND TERMINAL VOLTAGE This resistance behaves as though it were in series with the emf.
RESISTORS IN SERIES AND IN PARALLEL A series connection has a single path from the battery, through each circuit element in turn, then back to the battery.
RESISTORS IN SERIES AND IN PARALLEL The current through each resistor is the same; the voltage depends on the resistance. The sum of the voltage drops across the resistors equals the battery voltage.
RESISTORS IN SERIES AND IN PARALLEL From this we get the equivalent resistance (that single resistance that gives the same current in the circuit).
RESISTORS IN SERIES AND IN PARALLEL A parallel connection splits the current; the voltage across each resistor is the same:
RESISTORS IN SERIES AND IN PARALLEL The total current is the sum of the currents across each resistor:
RESISTORS IN SERIES AND IN PARALLEL This gives the reciprocal of the equivalent resistance:
RESISTORS IN SERIES AND IN PARALLEL An analogy using water may be helpful in visualizing parallel circuits:
KIRCHHOFF S RULES Some circuits cannot be broken down into series and parallel connections.
KIRCHHOFF S RULES For these circuits we use Kirchhoff s rules. Junction rule: The sum of currents entering a junction equals the sum of the currents leaving it.
KIRCHHOFF S RULES Loop rule: The sum of the changes in potential around a closed loop is zero.
KIRCHHOFF S RULES Problem Solving: Kirchhoff s Rules 1. Label each current. 2. Identify unknowns. 3. Apply junction and loop rules; you will need as many independent equations as there are unknowns. 4. Solve the equations, being careful with signs.
EMFS IN SERIES AND IN PARALLEL; CHARGING A BATTERY EMFs in series in the same direction: total voltage is the sum of the separate voltages
EMFS IN SERIES AND IN PARALLEL; CHARGING A BATTERY EMFs in series, opposite direction: total voltage is the difference, but the lower-voltage battery is charged.
EMFS IN SERIES AND IN PARALLEL; CHARGING A BATTERY EMFs in parallel only make sense if the voltages are the same; this arrangement can produce more current than a single emf.
CIRCUITS CONTAINING CAPACITORS IN SERIES AND IN PARALLEL Capacitors in parallel have the same voltage across each one:
CIRCUITS CONTAINING CAPACITORS IN SERIES AND IN PARALLEL In this case, the total capacitance is the sum:
EMFS IN SERIES AND IN PARALLEL; CHARGING A BATTERY Capacitors in series have the same charge:
EMFS IN SERIES AND IN PARALLEL; CHARGING A BATTERY In this case, the reciprocals of the capacitances add to give the reciprocal of the equivalent capacitance:
RC CIRCUITS RESISTOR AND CAPACITOR IN SERIES When the switch is closed, the capacitor will begin to charge.
RC CIRCUITS RESISTOR AND CAPACITOR IN SERIES The voltage across the capacitor increases with time: This is a type of exponential.
RC CIRCUITS RESISTOR AND CAPACITOR IN SERIES The charge follows a similar curve: This curve has a characteristic time constant:
RC CIRCUITS RESISTOR AND CAPACITOR IN SERIES If an isolated charged capacitor is connected across a resistor, it discharges: Q = Q 0 e -t/rc
ELECTRIC HAZARDS Even very small currents 10 to 100 ma can be dangerous, disrupting the nervous system. Larger currents may also cause burns. Household voltage can be lethal if you are wet and in good contact with the ground. Be careful!
ELECTRIC HAZARDS A person receiving a shock has become part of a complete circuit.
ELECTRIC HAZARDS Faulty wiring and improper grounding can be hazardous. Make sure electrical work is done by a professional.
ELECTRIC HAZARDS The safest plugs are those with three prongs; they have a separate ground line. Here is an example of household wiring colors can vary, though! Be sure you know which is the hot wire before you do anything.
AMMETERS AND VOLTMETERS MEASUREMENT AFFECTS THE QUANTITY BEING MEASURED An ammeter measures current; a voltmeter measures voltage. Both are based on galvanometers, unless they are digital. The current in a circuit passes through the ammeter; the ammeter should have low resistance so as not to affect the current.
AMMETERS AND VOLTMETERS MEASUREMENT AFFECTS THE QUANTITY BEING MEASURED A voltmeter should not affect the voltage across the circuit element it is measuring; therefore its resistance should be very large.
AMMETERS AND VOLTMETERS MEASUREMENT AFFECTS THE QUANTITY BEING MEASURED An ohmmeter measures resistance; it requires a battery to provide a current
AMMETERS AND VOLTMETERS MEASUREMENT AFFECTS THE QUANTITY BEING MEASURED If the meter has too much or (in this case) too little resistance, it can affect the measurement.
SUMMARY A source of emf transforms energy from some other form to electrical energy A battery is a source of emf in parallel with an internal resistance Resistors in series: Resistors in parallel:
SUMMARY Kirchhoff s rules: sum of currents entering a junction equals sum of currents leaving it total potential difference around closed loop is zero
SUMMARY Capacitors in parallel: Capacitors in series:
SUMMARY RC circuit has a characteristic time constant: To avoid shocks, don t allow your body to become part of a complete circuit Ammeter: measures current Voltmeter: measures voltage