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Problem 39 Easy Difficulty

Consider the circuit of Fig. E25.30. (a) What is the total rate at which electrical energy is dissipated in the 5.0-$\Omega$ and 9.0-$\Omega$ resistors? (b) What is the power output of the 16.0-V battery? (c) At what rate is electrical energy being converted to other forms in the 8.0-V battery? (d) Show that the power output of the 16.0-V battery equals the overall rate of consumption of electrical energy in the rest of the circuit.


A. $3.1 \mathrm{W}$
B. $7.2 \mathrm{W}$
C. $4.1 \mathrm{W}$
D. $(b)=(a)+(c)$


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Video Transcript

in the first part of this problem, we're going to calculate the write off in energy dissipation. That is a be The participation is written as P is equal to power dissipation along the resistor for five home which will be I square are five last yet I squared our night Well, this high square are nine. Is the participation along the resistor off resistance? Uh, mine. Oh my God, by inserting well is into the squad and we can write this one as a P is equals to I square, which is equals to zero point 47 unbearable square in tow are five features equals to 5.0 mega plus 9.0 omega. So from here we can wide this PSP's equals two 3.1 word. In second part of this problem, we're going to calculate the power output off the battery that is a pee wee. In order to calculate the power output, we use the question PV is equals to, uh, he I minus said I square are where this is the email from the battery and, uh, this artist, the internal resistance How? By inserting words into this question, we can ride this period as periods equals two e, which is equals to 16 world into I, which is equals to 0.47 and bad minus into 0.47 and pair all square into our which is goals to 1.6 omega. So from here we can ride this PBS PBS equals to seven point. To what? In parts of this problem, we have to show that the power output off the battery is equal to the oral read off convention that is, a TV is equal to p five plus B nine plus p EDT. Well, the spirit is not far off. Eight volt battery. Now this can be written as a seven point toward is equals to 1.1. What plus 2.0 plus are be it. We call it the question number one. What skill player? This P EDT we can wide p it is equals to e I minus plus I square are so by inserting will use into this question we can write this Pierre is equals to into 8.0 world into 0.47 I'm bad mind Plus in 20.47 and bad all square into 1.4 mega. So this will be PRD's equals two 4.1 word. Now inserting this we're living to equation about one. We can show that some point to it it's equals to seven point toward hands proved end of the question. Thank you.

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