PHY2054: Chapter 18 - Electric Circuits Analysis, Study notes of Physics

Download PHY2054: Chapter 18 - Electric Circuits Analysis and more Study notes Physics in PDF only on Docsity! PHY2054: Chapter 18 34 Wheatstone Bridge An ammeter A is connected between points a and b in the circuit below, in which the four resistors are identical. What is the current through the ammeter? a) I / 2 b) I / 4 c) zero d) need more information The parallel branches have the same resistance, so equal currents flow in each branch. Thus (a) and (b) are at the same potential and there is no current flow across the ammeter. PHY2054: Chapter 18 35 Circuit Problem (1) The light bulbs in the circuit are identical. What happens when the switch is closed? (a) both bulbs go out (b) the intensity of both bulbs increases (c) the intensity of both bulbs decreases (d) A gets brighter and B gets dimmer (e) nothing changes Before: Potential at (a) is 24V, but so is potential at (b) because equal resistance divides 48V in half. When the switch is closed, nothing will change since (a) and (b) are still at same potential. PHY2054: Chapter 18 38 Res-Monster Maze All batteries are 4V All resistors are 4Ω Find current in R. (Hint: Find voltages along path not connected by resistors) PHY2054: Chapter 18 39 Res-Monster Maze All batteries are 4V All resistors are 4Ω Find current in R. (Hint: Find voltages along path not connected by resistors) 2 PHY2054: Chapter 18 40 Res-Monster Maze (Part 2) All batteries are 4V All resistors are 4Ω Find currents across these resistors PHY2054: Chapter 18 43 2 1 2 011 3 1 0 1 1 1 0 1 1 1 111 4 1 12 3 8 4677 9 1 9 8 10 0 12 11 1 10 9 9 9 0 0 0 Continue using junction rules until finished 1 3 2 PHY2054: Chapter 18 44 Light Bulbs A three-way light bulb contains two filaments that can be connected to the 120 V either individually or in parallel. A three-way light bulb can produce 50 W, 100 W or 150 W, at the usual household voltage of 120 V. What are the resistances of the filaments that can give the three wattages quoted above? Use P = V2/R R1 = 1202/50 = 288Ω (50W) R2 = 1202/100 = 144Ω (100W) PHY2054: Chapter 18 45 Problem What is the maximum number of 100 W light bulbs you can connect in parallel in a 100 V circuit without tripping a 20 A circuit breaker? (a) 1 (b) 5 (c) 10 (d) 20 (e) 100 Each bulb draws a current of 1A. Thus only 20 bulbs are allowed before the circuit breaker is tripped. PHY2054: Chapter 18 48 Find Currents (3) Total current I = 11.70, find current I2 One approach, find VA – VB VB = 0, VA = 60 – 3.00*11.70 = 24.90 I2 = 24.9 / 3.00 = 8.30 A 60 I1 I I2 A B C PHY2054: Chapter 18 49 Find Currents (4) Find I1 I1 = I – I2 = 3.40 Find remaining currents Find ΔV = VA - VC VC = 0 + 3.40*4.00 = 13.60 ΔV = 24.90 – 13.60 = 11.30 I10 = 11.30 / 10 = 1.13 I5 = 11.30 / 5 = 2.26 60 I1 I I2 A B C PHY2054: Chapter 18 50 Find Currents (5) Find remaining currents Use I1 = 3.40 Find ΔV = VA - VC VC = 0 + 3.40*4.00 = 13.60 ΔV = 24.90 – 13.60 = 11.30 I10 = 11.30 / 10 = 1.13 I5 = 11.30 / 5 = 2.26 60 I1 I I2 A B C PHY2054: Chapter 18 53 Charge and Current vs Time (For Initially Uncharged Capacitor) ( ) ( )/0 1 t RCq t q e−= − ( ) /0 t RCi t i e−= PHY2054: Chapter 18 54 RC Example Let V = 12 volts, C = 6μF, R = 100Ω τ = RC = 600μs Charge vs time Using units of μC and μsec Current vs time Using units of amps and μsec This circuit will fully charge in a few millisec ( ) ( )/ / 6001 72 1t RC tq CV e e− −= − = − / / 6000.12t RC tVi e e R − −= = PHY2054: Chapter 18 55 Exponential Behavior t = RC is the “characteristic time” of any RC circuit Only t / RC is meaningful t = RC Current falls to 37% of maximum value Charge rises to 63% of maximum value t =2RC Current falls to 13.5% of maximum value Charge rises to 86.5% of maximum value t =3RC Current falls to 5% of maximum value Charge rises to 95% of maximum value t =5RC Current falls to 0.7% of maximum value Charge rises to 99.3% of maximum value