TBR Physics Chapter 9 passage 7

[Perseverance7779311]

The question reads, "If only switch C is closed in circuit X, what is the current through resistor VI, if the battery has voltage V=12 volts, Rv=3ohms, Rvi=6 ohms, and Rvii=22 ohms?"

Background info:Rv and Rvi are in parallel. Rvii is in series with Rv and Rvi

I calculated that Req= 2 ohms and the Rtot=4 ohms. I calculated the current as 12V/4 ohms=3A. Im just confused on how the answer is supposed to be 1 A. Could someone please assist me. Thank you!

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[Cawolf]

I don't see that question in my passage 7, maybe you can post the page/question number. . .

There is likely something with the switches that we would need to see.

 

[Perseverance7779311]

@Cawolf, oh really....yea its question 49 in my book, pg 201 (2009 edition).

 

[Cawolf]

Must be a different edition then - my pg 201 is not a passage (2013 edition).

 

[techfan]

The question reads, "If only switch C is closed in circuit X, what is the current through resistor VI, if the battery has voltage V=12 volts, Rv=3ohms, Rvi=6 ohms, and Rvii=22 ohms?"

Background info:Rv and Rvi are in parallel. Rvii is in series with Rv and Rvi

I calculated that Req= 2 ohms and the Rtot=4 ohms. I calculated the current as 12V/4 ohms=3A. Im just confused on how the answer is supposed to be 1 A. Could someone please assist me. Thank you!

I don't have the book, but if the battery is in series with the first resistor (RVii (and I hope you meant 2 ohms and not 22)) and then that resistor is in series with Rv and Rvi which are in parallel with one another. then you need to find the voltage drop over Rvii (since voltage drops over resistors in series, but current is constant). To do that you find the equivalent resistance of Rv and Rvi which is 1/6+1/3=1/Req and like you said Req=2. Then you have to find the amount of voltage that drops over Rvii which is Vout=Vin*(R2/(R1+R2)) where Vin is the initial voltage R1 is the first resistor you come across (in this case Rvii) and R2 is the 2nd resistor you come across in series (in this case Req).

That gives:
Vout=12V*(2/(2+2))=6V which is the voltage that the resistors in series sees (voltage is constant for resistors in parallel, but current splits).

Since the current splits for resistors in parallel (Rv and Rvi), you simply use V=IR for each resistor to solve for the current.

So for Rvi, V=6V R= 6 ohms, and I=V/R; I=6V/6 ohm=1 A

next time consider taking a picture with your phone, or if you have the PDF use the snipping tool (search for snipping tool in Windows Vista,7, 8 after hitting the windows key)

 

[Perseverance7779311]

@techfan, thank you very much...that helps!!