Electric Circuits 1 Electric Current and Electromotive Force The flow of electric charges Electric currents power light bulbs TV sets computers etc Definition of electric current The current is the rate at which charge flows through a surface perpendicular to the flow I q t 1 SI unit ampere A 1 A 1 C s It is conventional to give the current the same direction as the flow of positive charge Dr D Wackeroth Spring 2005 PHY102A Electric Circuits Circuits The transfer of electric energy in form of kinetic energy of the moving charge carriers takes place via electric circuits A circuit consists of an energy source e g battery generator and energy consuming devices e g light bulb TV computer which are connected by conducting wires emf source that maintains a constant current in a closed circuit The name originates from electromotive force The emf is the maximum potential difference provided by the source direct current dc circuits charges move around circuits in the same direction at all times battery alternating current ac circuits the direction of charges moving around a circuit changes from momemt to moment generators at power companies Dr D Wackeroth Spring 2005 PHY102A Electric Circuits 2 Resistance and Ohm s Law When a voltage V is applied across a piece of material the current I is found to be proportional to the applied voltage The ratio V I is called the resistance R of the material For many materials including most metals the resistance is constant over a wide range of applied voltages When the resistance is constant Ohm s law applies V R constant I or V RI 2 SI unit ohm 1 1 V A Ohm s law is an empirical relationship Dr D Wackeroth Spring 2005 PHY102A Electric Circuits 3 Resistivity In a metal conductor the electric current is carried by moving electrons Resistance originates from collisions of these electrons with atoms The resistance of an ohmic conductor is proportional to its length L and inversely proportional to its cross sectional area A L A is called the resistivity of the material R 3 depends on the electronic structure of the material and the temperature good conductors have a small resistivity good insulators have a high resistivity Eq 3 is analogous to the flow of a liquid through a pipe Dr D Wackeroth Spring 2005 PHY102A Electric Circuits Temperature variation of resistance For most metals resistivity increases approximately linearly with temperature over a limited temperature range 0 1 T T0 4 0 is the resistivity at a reference temperature T0 usually 20 C is the resistivity at a temperature T and is the temperature coefficient of resistivity Since R is proportional to R R0 1 T T0 5 0 R increases with increasing temperature metals 0 R decreases with increasing temperature semiconductors Dr D Wackeroth Spring 2005 PHY102A Electric Circuits 4 Superconductors There is a class of metals and compounds whose resistances suddenly go virtually to zero below a critical temperature T These materials are called superconductors Once a current is set up in a superconductors it persists without any applied voltage R 0 For most metals T is typically a few K For certain compounds such as Y Ba2 Cu3 O7 T is about 100 K These materials are called high T superconductors Is there superconductivity at room temperature Dr D Wackeroth Spring 2005 PHY102A Electric Circuits 5 Electrical Energy and Power Battery chemical energy stored in the battery is continuously transformed into kinetic energy of the charge carriers through the electric potential difference at the and terminals of the battery This kinetic energy is quickly lost due to collisions between the charge carriers and the atoms ions in a resistor temperature of conductor increases chemical energy is transformed into thermal energy Note we neglect the resistance of the thin wires connecting the battery and the resistor Dr D Wackeroth Spring 2005 PHY102A Electric Circuits Rate at which a charge q loses energy when it passes through a resistor V is the voltage q V IV 6 t Rate of energy change Power P P IV 7 or with Ohm s law V RI P I 2R V2 R 8 Example space heater P 2 kW V 120 V operating for 5 min 2 R 7 2 q 16 7 A I energy P t 2 kW 300s 6 105 J 0 167 kW h Conversion factor 1kW h 3 6 106 J Dr D Wackeroth Spring 2005 PHY102A Electric Circuits 6 Resistors in Series Consider two resistors R1 and R2 connected to a battery in a circuit called a series circuit series circuit there is only one pathway for the electric current Total potential difference V IR1 IR2 9 Note the same current I is flowing through both resistors because we consider a series circuit Dr D Wackeroth Spring 2005 PHY102A Electric Circuits R1 and R2 can be replaced with an equivalent resistor R Apply Ohm s law V IR IR1 IR2 10 R R1 R2 11 For three or more resistors connected in series R R1 R2 R3 12 Note The equivalent resistance of a series combination of resistors is always greater than any individual resistance Dr D Wackeroth Spring 2005 PHY102A Electric Circuits 7 Resistors in Parallel Consider two resistors R1 and R2 connected in parallel When resistors are connected in parallel the potential differences voltages across them are the same Dr D Wackeroth Spring 2005 PHY102A Electric Circuits Since charge is conserved the current I which enters point a must equal the total current leaving that point I1 I2 I I 1 I2 Apply Ohm s law to each resistor I1 and to the equivalent resistor I 1 13 I2 V V V R R1 R2 2 14 Therefore 1 1 1 R R1 R2 15 For 3 or more resistors in parallel 1 1 1 1 R R1 R2 R3 Dr D Wackeroth Spring 2005 16 PHY102A Electric Circuits Remarks The equivalent resistance of 2 or more resistors connected in parallel is always less than the smallest resistance in the group Household circuits are always wired so that appliances are connected in parallel Each device operates independently and each receives the same voltage Problem solving Strategy Resistors 1 When 2 or more resistors are connected in series they carry the same current but the voltages across them are different The resistances add directly to give the equivalent resistance of the series combination 2 When 2 or more resistors are connected in parallel the voltages across them are the same The equivalent resistance of a parallel combination of resistors is found through reciprocal addition Dr D Wackeroth Spring 2005 PHY102A Electric Circuits 3 A complicated circuit consisting of resistors can often be reduced to a simple circuit with only one equivalent resistor To do so a replace any resistors in