PHY2054: Chapter 1833Circuit Problem (1)ÎThe 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 changesBefore: Potential at (a) is 24V, but sois potential at (b) because equalresistance divides 48V in half. When theswitch is closed, nothing will changesince (a) and (b) are still at same potential.PHY2054: Chapter 1834Circuit Problem (2)ÎBulbs A and B are identical. What happens when the switch is closed? (a) nothing happens (b) A gets brighter, B dimmer (c) A gets dimmer, B brighter (d) Both A and B get brighter (e) Both A and B get dimmerBefore: Bulb A and bulb B both have 9V across them.After: Bulb A has 12V across it andbulb B has 6V across it (these potentials are forced by the batteries).PHY2054: Chapter 1835Calculate Currents2132112 3 063 0iiiii=++− =+− =1221342422iii===−=PHY2054: Chapter 1836Res-Monster MazeAll batteries are 4VAll resistors are 4ΩFind current in R. (Hint: Find voltagesalong path not connected by resistors)2PHY2054: Chapter 1837Res-Monster Maze (Part 2)All batteries are 4VAll resistors are 4ΩFind currents acrossthese resistorsPHY2054: Chapter 1838Light Bulbs ÎA 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/R¾R1= 1202/50 = 288Ω (50W)¾R2= 1202/100 = 144Ω (100W)PHY2054: Chapter 1839ProblemÎWhat 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) 100Each bulb draws a current of 1A. Thus only 20 bulbs are allowed before the circuit breaker is tripped.PHY2054: Chapter 1840VRC CircuitsÎCharging a capacitor takes time in a real circuit Resistance allows only a certain amount of current to flow Current takes time to charge a capacitorÎAssume uncharged capacitor initially Close switch at t = 0 Initial current is (no charge on capacitor)ÎCurrent flows, charging capacitor Generates capacitor potential of q/CÎCurrent decreases continuously as capacitor charges! Goes to 0 when fully charged/iVR=resistor/VVqCRiΔ=−=iPHY2054: Chapter 1841Analysis of RC CircuitsÎCurrent and charge are relatedÎSo can recast previous equation as “differential equation“ÎGeneral solution is (Check and see!) K = −CV (necessary to make q = 0 at t = 0)ÎSolve for charge q and current i/idqdt=dq q Vdt RC R+=/tRCqCVKe−=+()//1tRC tRCdq VqCV e i edt R−−=− ==/VqCRi−=PHY2054: Chapter 1842Charge and Current vs Time(For Initially Uncharged Capacitor)()()/01tRCqt q e−=−()/0tRCit ie−=PHY2054: Chapter 1843Exponential BehaviorÎt = RC is the “characteristic time” of any RC circuit Only t / RC is meaningfulÎt = RC Current falls to 37% of maximum value Charge rises to 63% of maximum valueÎt =2RC Current falls to 13.5% of maximum value Charge rises to 86.5% of maximum valueÎt =3RC Current falls to 5% of maximum value Charge rises to 95% of maximum valueÎt =5RC Current falls to 0.7% of maximum value Charge rises to 99.3% of maximum valuePHY2054: Chapter 1844Discharging a CapacitorÎConnect fully charged capacitor to a resistor at t = 0ÎGeneral solution is K = CV (necessary to make have full charge at t = 0)ÎSolve for charge q and current iR0qiRC−−=0dq qdt RC+=/tRCqKe−=///0tRC tRC tRCdq VqCVe i e Iedt R−−−= = =− =−CSPHY2054: Chapter 1845Charge and Current vs Time(For Initially Charged Capacitor)()/0tRCqt qe−=()/0tRCit
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