a) Determine the equivalent resistance of the “ladder” of equal 175-\Omega resistors shown in Fig. 19–49. In other words, what resistance would an ohmmeter read if connected between points A and B? b) What is the current through each of the three resistors on the left if a 50.0-V battery is connected between points A and B?

a) 478 \; \Omega b) I_T = I_B = 0.105 A, I_m = 0.0767 A

Giancoli 7th Edition, Chapter 19, Problem 18

Problem 18

Determine the equivalent resistance of the “ladder” of equal $175$ - $\Omega$ resistors shown in Fig. 19–49. In other words, what resistance would an ohmmeter read if connected between points A and B?
What is the current through each of the three resistors on the left if a 50.0-V battery is connected between points A and B?

Figure 19-49.

$478 \; \Omega$
$I_T = I_B = 0.105 \textrm{ A, } I_m = 0.0767 \textrm{ A}$

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COMMENTS

By saie.joshi on Sun, 2/5/2017 - 7:21 PM

do the nodes initially not mean anything then? I thought the nodes would make the resistors not in parallel or series.

By Mr. Dychko on Sun, 2/5/2017 - 8:24 PM

Hi saie.joshi,

Thanks for the question. This diagram is a bit tricky since some resistors are in series, whereas others are in parallel. We break it down step by step. If current reaching a node has a choice between multiple paths, then the resistors along the two (or more) paths are in parallel. If current reaching a node has only one option, and that is to proceed through another resistor, then that next resistor is in series. Does that help?

All the best,
Mr. Dychko

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