Physics 161 Lecture 23: electric current, Ohm's law, circuits and power November 18, 2014 1 review • • ! • • "electric potential" (V) = electric potential energy per unit charge. units : V(volt) = J/C = Nm/C parallel plates with +Q on top plate and -Q on the lower. potential across the plates: V = Ed Make analogy with constant force gravitational potential gh ! Capacitance: V = Q/C. ! • stored energy in a capacitor: (1/2)CV2 = (1/2)Q2/C ! ! • capacitors and energy storage kinds of capacitors: parallel plate (air gap, dielectric) 2 Capacitors with Dielectrics If an insulating material (a dielectric) is inserted between the capacitor plates, the capacitance is increased A C = k✏0 d where k is the dielectric constant of the material k is nearly always greater than 1 For a given charge Q on the plates, the electric field between the plates and therefore the voltage difference across the plates will be less 3 current current (I) = amount of flowing charge per unit time ! measured in units of C/s = A(ampere) ! Let charges flow with "drift velocity" vd in a wire with cross sectional area A I = qvdnA, where q = charge of electron, n = density of electrons ! ! How big is v? Note on the sign of current: ! When electrons flow left to right, it is equivalent to positive charge flow right to left. 4 clicker question In a 1 A current flow, about how many electrons are passing per second? One electron has a charge of 1.6x10-19 C. (a) 1 (b) 10-19 (c) 1019 (d) 1010 5 battery How is current produced? battery! Battery provides electric potential for moving positive charge in the external circuit from (+) terminal to (-) terminal. V + - E 6 How is I related to applied V? V Vary(indicated by ) V and measure I. I non-Ohmic behavior I Ohm’s law I V V 7 mechanism of Ohmic behavior Recall: think positive charge moving To move charge, E field is needed E force from E field and resistive force force only from E field in steady state: where R = … (not realistic) 8 series and parallel circuits Rtot = R1 + R2 +R3 1/Rtot = 1/R1 + 1/R2 9 clicker questions A current I passes through the resistor R which is connected in parallel with R/2. How much current is there in R/2? (a) I (b) 2I (c) I/2 (d) I/4 (e) The values of R and V must be known to determine. How much current is there in R on the left side? (a) I (b) 2I (c) 3I (d) I/3 (e) The values of R and V must be known to determine. 10 R/2 R R V power dissipation Apply E across a wire with area A, length d. N = nAd = total no. of charges n = no. charges/unit volume units: J/s = W (watt) P can also be rewritten as: 11 AC and DC DC (direct current) current flowing in one direction only example: battery AC(alternating current) current flowing in two directions alternately example: house current at 60 Hz. meaning of 110VAC: Vrms. 12 demo - clicker question When light two identical light bulbs are connected in series to the wall outlet, why do they become dimmer? (a)The voltage from the wall outlet becomes smaller. (b)The resistance of the light bulb changes. (c)The current passing through the bulb decreases. (d)The power dissipated in the light bulbs increases. (e)The light bulbs must be defective. When light two identical light bulbs are connected in series to the wall outlet, what is power dissipated in each bulb? Let P = power dissipated with one bulb connected alone. (a) P (b) P/2 (c) P/4 (d) P/16 13