An ideal voltmeter connected across a certain fresh 9-V battery reads 9.30 V, and an ideal ammeter briefly connected across the same battery reads 3.70 A. We say the battery has an open-circuit voltage of 9.30 V and a short-circuit current of 3.70 A. Model the battery as a source of emf ε in series with an internal resistance r as in Figure 27.1a. Determine both (a) ε and (b) r. An experimenter connects two of these identical batteries together as shown in Figure P27.45. Find (c) the open-circuit voltage and (d) the short-circuit current of the pair of connected batteries. (e) The experimenter connects a 12.0-Ω resistor between the exposed terminals of the connected batteries. Find the current in the resistor. (f) Find the power delivered to the resistor. (g) The experimenter connects a second identical resistor in parallel with the first. Find the power delivered to each resistor. (h) Because the same pair of batteries is connected across both resistors as was connected across the single resistor, why is the power in part (g) not the same as that in part (f)?
Figure P27.45
(a)
Answer to Problem 28.74AP
Explanation of Solution
Given info: The open circuit voltage of the battery is
In an open circuit current the current of the battery is
Formula to calculate the emf of the battery is,
Here,
Substitute
Conclusion:
Therefore, the emf of the battery is
(b)
Answer to Problem 28.74AP
Explanation of Solution
Given info: The open circuit voltage of the battery is
Formula to calculate the internal resistance of the battery is,
Here,
Substitute
Conclusion:
Therefore, resistance of the battery is
(c)
Answer to Problem 28.74AP
Explanation of Solution
Given info: The open circuit voltage of the battery is
Formula to calculate the total emf of the battery is,
Here,
Substitute
The total emf of the battery is equal to the open circuit voltage of the battery.
Conclusion:
Therefore, the open circuit voltage of the battery is
(d)
Answer to Problem 28.74AP
Explanation of Solution
Given info: The open circuit voltage of the battery is
The total resistance in the battery is,
Here,
Substitute
Thus, the internal resistance of the battery is
Formula to calculate the short circuit current of the batteries is,
Here,
Substitute
Conclusion:
Therefore, the short circuit current of the pair of connected batteries is
(e)
Answer to Problem 28.74AP
Explanation of Solution
Given info: The open circuit voltage of the battery is
The total series resistance in the battery is,
Here,
Substitute
Thus, the total series resistance of the battery is
Formula to calculate the current in the resistor
Here,
Substitute
Conclusion:
Therefore, the current in the resistor
(f)
Answer to Problem 28.74AP
Explanation of Solution
Given info: The open circuit voltage of the battery is
Formula to calculate the power delivered to the resistor is,
Here,
Substitute
Conclusion:
Therefore, the power delivered to the resistor is
(g)
Answer to Problem 28.74AP
Explanation of Solution
Given info: The open circuit voltage of the battery is
The batteries are connected in series. The voltages of the both batteries are same.
The equivalent internal resistance in the battery is,
Here,
Substitute
Thus, the total resistance of the resistor is
Formula to calculate the current in the batteries is,
Here,
Substitute
Thus, the current produced in the batteries is
Formula to calculate the terminal voltage across both batteries is,
Here,
Substitute
Thus, the terminal voltage across both batteries is
Formula to calculate the power delivered to each resistor is,
Here,
Substitute
Conclusion:
Therefore, the power delivered to each resistor is
(h)
Answer to Problem 28.74AP
Explanation of Solution
Given info: The open circuit voltage of the battery is
In part (g), the total internal resistance of the resistor is
Conclusion:
Therefore, the internal resistance of the batteries and the terminal voltage of the batteries is not same in both cases.
Want to see more full solutions like this?
Chapter 28 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
- In a scene from The Avengers (the first one) Black Widow is boosted directly upwards by Captain America, where she then grabs on to a Chitauri speeder that is 15.0 feet above her and hangs on. She is in the air for 1.04 s. A) With what initial velocity was Black Widow launched? 1 m = 3.28 ft B) What was Black Widow’s velocity just before she grabbed the speeder? Assume upwards is the positive direction.arrow_forwardIn Dark Souls 3 you can kill the Ancient Wyvern by dropping on its head from above it. Let’s say you jump off the ledge with an initial velocity of 3.86 mph and spend 1.72 s in the air before hitting the wyvern’s head. Assume the gravity is the same as that of Earth and upwards is the positive direction. Also, 1 mile = 1609 m. A) How high up is the the ledge you jumped from as measured from the wyvern’s head? B) What is your velocity when you hit the wyvern?arrow_forwardA) If Yoshi flings himself downwards at 9.76 miles per hour to hit an enemy 10.5 m below him, how fast is Yoshi traveling when he hits the enemy? 1 mile = 1609 marrow_forward
- Two objects get pushed by the same magnitude of force. One object is 10x more massive. How does the rate of change of momentum for the more massive object compare with the less massive one? Please be able to explain why in terms of a quantitative statement found in the chapter.arrow_forwardA box is dropped on a level conveyor belt that is moving at 4.5 m/s in the +x direction in a shipping facility. The box/belt friction coefficient is 0.15. For what duration will the box slide on the belt? In which direction does the friction force act on the box? How far will the box have moved horizontally by the time it stops sliding along the belt?arrow_forwardNo chatgpt pls will upvotearrow_forward
- No chatgpt pls will upvotearrow_forwardA toy car speeds up at 1.0 m/s2 while rolling down a ramp, and slows down at a rate of 2.0 m/s2 while rolling up the same ramp. What is the slope of the ramp in degrees? Grade in %? The friction coefficient?arrow_forwardPlz solution should be complete No chatgpt pls will upvote .arrow_forward
- College PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning