An external resistor with resistance R is connected to a battery that has emf ε and internal resistance r. Let P be the electrical power output of the source. By conservation of energy, P is equal to the power consumed by R. What is the value of P in the limit that R is (a) very small; (b) very large? (c) Show that the power output of the battery is a maximum when R = r. What is this maximum P in terms of ε and r? (d) A battery has ε = 64.0 V and r = 4.00 Ω. What is the power output of this battery when it is connected to a resistor R, for R = 2.00 Ω, R = 4.00 Ω, and R = 6.00 Ω? Are your results consistent with the general result that you derived in part (b)?
Want to see the full answer?
Check out a sample textbook solutionChapter 25 Solutions
University Physics with Modern Physics, Books a la Carte Edition; Modified MasteringPhysics with Pearson eText -- ValuePack Access Card -- for ... eText -- Valuepack Access Card (14th Edition)
Additional Science Textbook Solutions
University Physics Volume 2
College Physics: A Strategic Approach (4th Edition)
University Physics (14th Edition)
Conceptual Physics (12th Edition)
Physics for Scientists and Engineers with Modern Physics
Physics (5th Edition)
- The student engineer of a campus radio station wishes to verify the effectiveness of the lightning rod on the antenna mast (Fig. P21.71). The unknown resistance Rx is between points C and E. Point E is a true ground, but it is inaccessible for direct measurement because this stratum is several meters below the Earths surface. Two identical rods are driven into the ground at A and B, introducing an unknown resistance Ry. The procedure is as follows. Measure resistance R1 between points A and B, then connect A and B with a heavy conducting wire and measure resistance R2 between points A and C. (a) Derive an equation for Rx in terms of the observable resistances, R1 and R2. (b) A satisfactory ground resistance would be Rx 2.00 . Is the grounding of the station adequate if measurements give R1 = 13.0 and R2 = 6.00 ? Explain. Figure P21.71arrow_forwardA flashing lamp in a Christmas earring is based on an RC discharge of a capacitor through its resistance. The effective duration of the flash is 0.250 s, during which it produces an average 0.500 W from an average 3.00 V. (a) What energy does it dissipate? (b) How much charge moves through the lamp? (c) Find the capacitance, (d) What is the resistance of the lamp? (Since average values are given for some quantities, the shape of the pulse profile is not needed.)arrow_forwardA lightbulb is connected to a variable power supply. As the potential across the bulb is varied, the resulting current and the filaments temperature are measured. The data are listed in Table P28.38. a. Find R for each entry in Table P28.38, and then plot R as a function of T. b. Assume that room temperature is at 293 K. Find R0 (resistance at room temperature). Comment on your result.arrow_forward
- A student makes a homemade resistor from a graphite pencil 5.00 cm long, where the graphite is 0.05 mm indiameter. The resistivity of the graphite is =1.38102/m . The homemade resistor is place inseries with a switch, a 10.00-mF capacitor and a 0.50-V power source, (a) What is the BC time constant of the circuit? (b) What is the potential drop across the pencil 1.00 s after the switch is closed?arrow_forwardAn ECG monitor must have an KC time constant lessthan 1.00102s to be able to measure variations involtage oversmall time intervals, (a) If the resistance of the circuit (duemostly to that of the patient's chest) is 1.00kTwhat is the maximum capacitance of the circuit?(b) Would It be difficult in practice to limit the capacitance to less than the value found in (a)?arrow_forwardA network of two identical capacitors, each with capacitance C, is charged through a resistor R using a battery with emf E. (a) What is the time constant, in terms of R and C, for the charging circuit if the two capacitors are in series? (b) In parallel? (c) For which capacitor network, series or parallel, does the voltage across the resistor become 1% of its initial value in a shorter time?arrow_forward
- The figure below shows a capacitor, with capacitance C = 7.22 PF, and a resistor, with resistance R = 4.23 MQ, connected in series to a battery, with E = 28.0 V. The circuit has a switch, which is initially open. R (a) What is the circuit's time constant (in seconds)? (b) What is the maximum charge (in µc) on the capacitor after the switch is closed? (c) What is the current (in HA) through the resistor 10.0 s after the switch is closed?arrow_forwardIn the circuit shown in the figure, the S switch closed at t=0 and the capacitors, which are completely empty, begin to fill. Here ε=10 V, C=5 μF and R=55 Ω. What is the time constant of the circuit, τ, in units of microseconds? When t= τ, what is the total charge, in units of microcoulomb, accumulated in the capacitors?arrow_forwardYou are given the job of evaluating potential power line systems. One system is designed to operate at V = 3000 V, and another would operate at V = 6500 V. Suppose the power line at the higher voltage would dissipate 3 % of the power that it carries. What percentage of the power would be dissipated in the low-voltage power line?arrow_forward
- A capacitor that is initially uncharged is ocnnected in series with a resistor and an emf source with ℰ = 110 V and negligible internal resistance. Just after the circuit is completed, the current through the resistor is 6.5 × 10−5 A. The time constant for the circuit is 5.2 s. What are the resistance of the resistor and the capacitance of the capacitor?arrow_forwardThe capacitor in the figure has square plates with b meters on each side. Neglect fringing in the system. A square conducting slab is allowed to move between the two plates. The square surface of the slab also has b meters on each side. In addition, the slab has a height of h meters, and a negligible resistance. Capacitance in Coulombs is given by the following equation in all possible states of the capacitor. What is the magnitude of the electrostatic force?arrow_forwardThe potential difference across a charged capacitor is 16 V. The capacitor discharges through a fixed resistor. After a time equal to the time constant, the potential difference has reduced to V. The magnitude of V is:arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning