Practice question from book, solving circuit

[Tomer]

Hi,

I am missing something with this question and i am not getting a correct answer.

They are asking to calculate the Current on the 600Ohm resistor (R2)
1.png  - The circuit for the question.

I started by calculating the equivalent resistance and equivalent current of the circuit and i got:
I - 0.44A
R - 500Ohm

* I know that the total current in the circuit is the same current for the first resistor (100Ohm resistor)

I1 = 0.44A
Then i continued and found the Voltage for the 100Ohm resistor
V1 = 44V

Because the next resistors are in parallel i know that the voltage on them is the same.
So i thought that 220V - 44V should give me the Voltage on R2 and R3 (600Ohm and 300Ohm) resistors

But i am guessing this is not correct as i am getting that the current on R2(600Ohm) resistor is 0.12A and the correct answer is 0.5A




Appreciate help with what i am missing here.

Thank you,
Tom
 
 

[soldar]

Total current going around the circuit is 440 mA. This is correct.

Now the 300 ohm resistor will carry twice as much as the 600 ohm resistor. Divide 440 by three and 600 carries one part and 300 carries two parts.

Check by showing the voltage on bot resistors is the same.

[Paul Rose]

I spot one mistake with your (original poster, not Soldar) work.

The total current 0.44 A is correct ( the total 500 ohms was correct ).

But the voltage across the 600 ( and 300 ) ohm pair is not 220 - 44v.  You got the voltage at the top of the pair, but not at the bottom.

Juse use V=I x R to calculate the voltage drop across the combined 200 ohm:  0.44 x 200 = 88 volts

As you said, this voltage is the same across the 600 as the 300.

Use I = V / R to calculate the current through the 600:  I = 88 / 600 = 0.14666... Amperes.

This does not match your expected 0.5 A

[Tomer]

Thank you for the explanations, i understand the logic now and this is the key "You got the voltage at the top of the pair, but not at the bottom."


 

Tom

[rstofer]

Replace the top and bottom resistors with a single resistor equivalent to the sum (100+200=>300).  Combine the parallel resistors to get 200 Ohms and add it to this new equivalent resistor (300 Ohms) and calculate the current.  You come up with a single resistor of 500 Ohms and it's pretty easy to see why the current is 220/500 or 0.44A.

Now that you know the total current flow, it's easy to see that 1/3 goes through the 600 Ohm resistor and 2/3 through the 300 Ohm resistor.  So, 0.44/3 = 0.147A  Prove the current division by noting that the voltage drop across the 600 Ohm resistor is exactly the same as the drop across the 300 Ohm resistor given their respective currents (0.147A * 600 = 0.293A * 300, more or less due to roundoff).

I don't see how the proper answer can be 0.5A through the 600 Ohm resistor.

[vk6zgo]

Pretty obviously, the book answer is a typo.
Sadly, this is not unusual with text books, & is, if anything, becoming more prevalent.

[rstofer]

Maybe you just have to stand up for your answer!

You do the work, you solve the math and if you get a different answer, verify it with another approach and then just move on.  The book 'answer' is wrong and that's the end of it.

Here's another thought:  3 different people got the same answer and it doesn't agree with the book.  Chances are the book is wrong!

[Tomer]

Thank you for all the explanations and help!