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Chapter 27 - Circuits • To produce a steady flow of charge you need a ”charge pump” or electromotive force (emf) that does work on the charge carriers. One example of an emf device is a battery. Another such device is an electric generator. • The emf of an emf device is the work per unit charge that teh device does in moving charge from its low potential terminal to its high potential terminal - the SI unit is the Joule/Coulomb or the volt. ǫ= dW . dq • EMF is the ”theoretical” potential difference between the terminals of the device. In reality because of resistance, the actual potential difference between the terminals is not equal to the emf. • A battery is a device for producing a potential difference between its terminals. Again the convention is that arrows are drawn in a circuit pointing in the direction of positive charge, even though the electrons may move in the opposite direction. • Batteries are more complicated than you think. • The work done in moving charge dq is dW = ǫdq = ǫidt, ǫ = iR. • ǫ is the energy per unit charge transferred to the moving charges by the battery. iR is the energy per unit charge transferred from the moving charges to thermal energy within the circuit. • Loop Rule: The algebraic sum of the changes in potential encountered in a complete traversal of the loop of a circuit must be zero. • For a move through a resistance in the direction of the current, the change in potential is −iR; in the opposite direction it is +iR. • For a move through an ideal emf device in the direction of the emf arrow, the change in potential is +ǫ, in the opposite direction it is -ǫ. • Effective resistance of a series of resistors in series is Ref f = X Ri . The same current flows through resistors in series but the sum of the potential differences across each resistor is equal to the total potential difference across all resistors. 1 • To find the potential difference between any two points in a circuit, start at the one point and traverse the circuit to the other point, following any path and add algebraically the changes in potential you encounter. • Grounding a circuit at a particular point means that point in the circuit is connected to Earth and has potenital zero. • Net rate of energy transfer from thje emf device to the charge carriers is P = iV, where V is the potential across the terminals of the emf device: P = i(ǫ − ir). • Read through Sample Problem on p. 713. • Junction Rule: The sum of the currents entering any junction must be equal to the sum of the currents leaving that junction. • Resistors in Parallel - have different currents but the same voltage across them: X 1 1 = ( )) Ref f Ri • Read through Sample Problem p. 716. • Ammeter and Voltmeter • RC Circuit: q = Cǫ(1 − e−t/RC ), ǫ i = e−t/RC . R • A capacitor that is being charged initially acts like ordinary connecting wire relative to the charging current. A long time later, it acts like a broken wire. 2