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Chapter 25, Problem 25.78CP

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)?

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Chapter 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)

Ch. 25 - When is a 1.5-V AAA battery not actually a 1.5-V...Ch. 25 - Can the potential difference between the terminals...Ch. 25 - A rule of thumb used to determine the internal...Ch. 25 - Batteries are always labeled with their emf; for...Ch. 25 - We have seen that a coulomb is an enormous amount...Ch. 25 - Electrons in an electric circuit pass through a...Ch. 25 - Temperature coefficients of resistivity are given...Ch. 25 - Which of the graphs in Fig. Q25.12 best...Ch. 25 - Why does an electric light bulb nearly always burn...Ch. 25 - A light bulb glows because it has resistance. The...Ch. 25 - (See Discussion Question Q25.14.) An ideal ammeter...Ch. 25 - (See Discussion Question Q25.14.) Will a light...Ch. 25 - The energy that can be extracted from a storage...Ch. 25 - Eight flashlight batteries in series have an cmf...Ch. 25 - Small aircraft often have 24-V electrical systems...Ch. 25 - Long-distance, electric-power, transmission lines...Ch. 25 - Ordinary household electric lines in North America...Ch. 25 - A fuse is a device designed to break a circuit,...Ch. 25 - High-voltage power supplies are sometimes designed...Ch. 25 - The text states that good thermal conductors are...Ch. 25 - Lightning Strikes. During lightning strikes from a...Ch. 25 - A silver wire 2.6 mm in diameter transfers a...Ch. 25 - A 5.00-A current runs through a 12-gauge copper...Ch. 25 - An 18-gauge copper wire (diameter 1.02 mm) carries...Ch. 25 - Copper has 8.5 1028 free electrons per cubic...Ch. 25 - Prob. 25.6ECh. 25 - CALC The current in a wire varies with time...Ch. 25 - Current passes through a solution of sodium...Ch. 25 - BIO Transmission of Nerve Impulses. Nerve cells...Ch. 25 - (a) At room temperature, what is the strength of...Ch. 25 - A 1.50-m cylindrical rod of diameter 0.500 cm is...Ch. 25 - A copper wire has a square cross section 2.3 mm on...Ch. 25 - Prob. 25.13ECh. 25 - Prob. 25.14ECh. 25 - A cylindrical tungsten filament 15.0 cm long with...Ch. 25 - A ductile metal wire has resistance R. What will...Ch. 25 - Prob. 25.17ECh. 25 - Prob. 25.18ECh. 25 - Prob. 25.19ECh. 25 - Prob. 25.20ECh. 25 - A current-carrying gold wire has diameter 0.84 mm....Ch. 25 - A hollow aluminum cylinder is 2.50 m long and has...Ch. 25 - Prob. 25.23ECh. 25 - A carbon resistor is to be used as a thermometer....Ch. 25 - A copper transmission cable 100 km long and 10.0...Ch. 25 - Consider the circuit shown in Fig. E25.26. The...Ch. 25 - An ideal voltmeter V is connected to a 2.0-11...Ch. 25 - An idealized ammeter is connected to a battery as...Ch. 25 - When switch S in Fig. E25.29 is open, the...Ch. 25 - The circuit shown in Fig. E25.30 contains two...Ch. 25 - In the circuit shown in Fig. E25.30, the 16.0-V...Ch. 25 - In the circuit of Fig. E25.30, the 5.0- resistor...Ch. 25 - The circuit shown in Fig. E25.33 contains two...Ch. 25 - When a resistor with resistance R is connected to...Ch. 25 - Light Bulbs. The power rating of a light bulb...Ch. 25 - If a 75-W" bulb (see Problem 25.35) is connected...Ch. 25 - European Light Bulb. In Europe the standard...Ch. 25 - A battery-powered global positioning system (GPS)...Ch. 25 - Consider the circuit of Fig. E25.30. (a) What is...Ch. 25 - BIO Electric Eels. Electric eels generate electric...Ch. 25 - BIO Treatment of Heart Failure. A heart...Ch. 25 - The battery for a certain cell phone is rated at...Ch. 25 - Prob. 25.43ECh. 25 - An idealized voltmeter is connected across the...Ch. 25 - A 25.0- bulb is connected across the terminals of...Ch. 25 - A typical small flashlight contains two batteries,...Ch. 25 - In the circuit in Fig. E25.47, find (a) the rate...Ch. 25 - A 540-W electric heater is designed to operate...Ch. 25 - Prob. 25.49ECh. 25 - In an ionic solution, a current consists of Ca2+...Ch. 25 - An electrical conductor designed to carry large...Ch. 25 - An overhead transmission cable for electrical...Ch. 25 - On your first day at work as an electrical...Ch. 25 - A 2.0-m length of wire is made by welding the end...Ch. 25 - A 3.00-m length of copper wire at 20 C has a...Ch. 25 - A heating clement made of tungsten wire is...Ch. 25 - CP BIO Struck by Lightning. Lightning strikes can...Ch. 25 - A resistor with resistance R is connected to a...Ch. 25 - CALC A material of resistivity is formed into a...Ch. 25 - CALC The region between two concentric conducting...Ch. 25 - The potential difference across the terminals of a...Ch. 25 - (a) What is the potential difference Vad in the...Ch. 25 - BIO The average bulk resistivity of the human body...Ch. 25 - BIO A person with body resistance between his...Ch. 25 - A typical cost for electrical power is 0,120 per...Ch. 25 - In the circuit shown in Fig. P25.66, R is a...Ch. 25 - A Nonideal Ammeter. Unlike the idealized ammeter...Ch. 25 - A cylindrical copper cable 1.50 km long is...Ch. 25 - CALC A 1.50-m cylinder of radius 1.10 cm is made...Ch. 25 - Compact Fluorescent Bulbs. Compact fluorescent...Ch. 25 - Prob. 25.71PCh. 25 - CP Consider the circuit shown in Fig. P25.72. The...Ch. 25 - CP Consider the circuit shown in Fig. P25.73. The...Ch. 25 - DATA An external resistor R is connected between...Ch. 25 - DATA The voltage drop Vab across each of resistors...Ch. 25 - DATA According to the U.S. National Electrical...Ch. 25 - Prob. 25.77CPCh. 25 - An external resistor with resistance R is...Ch. 25 - BIO SPIDERWEB CONDUCTIVITY. Some types of spiders...Ch. 25 - BIO SPIDERWEB CONDUCTIVITY. Some types of spiders...Ch. 25 - BIO SPIDERWEB CONDUCTIVITY. Some types of spiders...Ch. 25 - BIO SPIDERWEB CONDUCTIVITY. Some types of spiders...
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