Steady State

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Electric Current • The amount of charge that flows by per unit time. Q • I t Steady state • A system (e.g. circuit) is in the steady state when the current at each point in the circuit is constant (does not change with time). – In many practical circuits, the steady state is achieved in a short time. • In the steady state, the charge (or current) flowing into any point in the circuit has to equal the charge (or current) flowing out. – Kirchhoff’s Node (or Current) Rule. n = number of charges per unit volume = “charge-number density” (n > 1027 m-3 for a good metal) -5 Figure 25.26 Typically vd ~ 10 m/s ~1 m/day Why do the electrons have a drift velocity? • They feel a force due to an electric field. • But then they should accelerate!: F = ma • Each electron does accelerate for some time but then it collides with something (a nucleus, another electron, etc.). • After the collision, the electron goes off in some random direction, giving it momentarily a zero average velocity. • The drift velocity is the average velocity in the a F qE v time between collisions: d 2 2mm 2 Which of the following statements is false? 1) An electric field is needed to produce an electric current. 2) A potential difference between two points is needed to produce an electric current. 3) For a steady current to flow in a wire, the wire must be part of a closed circuit. 4) The electric field is constant along all parts of the circuit when a steady current is flowing. 5) The electric current in a wire is proportional to the drift velocity of the charges. Ohm’s Law • Current through a resistor (ohmic device) is proportional to the potential difference across it. V IR qE v d 2m I qnAvd q2 nAE I 2m q2 nA V I 2ml Resistance and Resistivity • Resistance depends on the geometry of the resistor – its length and cross-sectional area – R is proportional to length – R is inversely proportional to area. rl R A • Resistivity r depends on material properties like how often charges scatter. Wire A, which is of the same length and material as wire B, has twice the diameter of wire B. If the resistance of wire B is R, what is the resistance of wire A? 1) R 2) 2R 3) R/2 4) 4R 5) R/4 Emf • Emf (Electromotive “force”) – the voltage provided by some voltage source (e.g. a battery). • A source of emf converts non-electrical energy to electrical energy. • E.g. electrical generator (turns mechanical energy into electrical) 1) I1R1 = I2R2 Which of the relations 2) I3R3 = I4R4 among the quantities in the 3) I R = I R figure is generally correct? 1 1 4 4 4) I3R4 = I4R3 5) I1R1 + I2R2 = e Power in a circuit E • Power: P t • In time t, a charge Q enters on the left and Q exits on the right. V b Va.

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