Circuit Question - Driving me crazy

[Allura]

Homework Statement

The problem is "What is the current through resistor g when switch B has been closed and switch A has been open for a long time?" (see diagram)

Homework Equations

V = IR
I/Reff = 1/R1 + 1/R2
Reff = R1 + R2

The Attempt at a Solution

Because f+g are in series, the Reff = 6 ohms. Since f/g is in parallel with c, the new Reff is 4 ohms. Then because f/g/c are in series with a/b, the new total resistance is 10 ohms. As a result, we can find through V = IR that the current is 9A (90 V = I x 10 ohms).

So then, if V = IR, to find the current through each respective resistor (in parallel), I did 90 V = I x 12 ohms, and 90 = I 6 ohms, however, this gives me currents that are incorrect. Instead, the answers are 6 A, and 3 A through the 6 ohm resistor and 12 ohm resistor. I understand this conceptually, i.e. yes, the resistor 12 ohm is 2X the resistor 6 ohm, therefore current would be half as large - however, I can't figure this out mathematically. Literally, I have spent an hour on this problem, I've read various tutorials, watched khanacademy, read the solution in the back of the book (which gives a conceptual answer) but I can't figure this out.

Please help, because I really want to figure this out and I can't move on until I do.

 

[Tanya Sharma]

Because f+g are in series, the Reff = 6 ohms. Since f/g is in parallel with c, the new Reff is 4 ohms. Then because f/g/c are in series with a/b, the new total resistance is 10 ohms. As a result, we can find through V = IR that the current is 9A (90 V = I x 10 ohms).

Correct till here .

So then, if V = IR, to find the current through each respective resistor (in parallel), I did 90 V = I x 12 ohms, and 90 = I 6 ohms,

The P.D across 12 and 6 Ω is not 90 V . Look carefully in the picture .

 

[Allura]

Correct till here .
The P.D across 12 and 6 Ω is not 90 V . Look carefully in the picture .

How do you find the potential difference? I thought it was the same between any set of resistors in series (i.e. only the current changes with differing resistances). Please help, at this point I am totally lost.

Thanks

 

[Tanya Sharma]

How do you find the potential difference? I thought it was the same between any set of resistors.

Thanks

You have correctly calculated the current 9A flowing through the battery.The current 9A from positive terminal of battery passes through the series combination of 'a' and 'b' and then divides in the parallel combination of 12 Ω and 6Ω (f+g) .

How does current divide in the parallel resistors ?

 

[Allura]

You have correctly calculated the current 9A flowing through the battery.The current 9A from positive terminal of battery passes through the series combination of 'a' and 'b' and then divides in the parallel combination of 12 Ω and 6Ω (f+g) .

How does current divide in the parallel resistors ?

I = V / R ? Then the currents add up to the total current, but I still can't get the right answers.

I know total current in is equal to the total current out..?

 

[Allura]

You have correctly calculated the current 9A flowing through the battery.The current 9A from positive terminal of battery passes through the series combination of 'a' and 'b' and then divides in the parallel combination of 12 Ω and 6Ω (f+g) .

How does current divide in the parallel resistors ?

I thought maybe, okay find a new voltage? But V= IR --> (9A) (4 ohms) where R = Total effective resistance. Then it's 36 V, so V = IR --> 36/12 = 3 A for c? Right?

But why do you find a new V and do the problem this way? But 4 ohms is for f, and not for C. I'm so confused :( :(

 

[Tanya Sharma]

The P.D across parallel resistors is same.

Let the potential difference across the parallel resistors 12 Ω and 6Ω be V .

Then V=I₁(12) and V=I₂(6) , where I₁+I₂ =9A .

Now solve for I₂ .

Does this make sense ?

 

[Allura]

The P.D across parallel resistors is same.

Let the potential difference across the parallel resistors 12 Ω and 6Ω be V .

Then V=I₁(12) and V=I₂(6) , where I₁+I₂ =9A

Does this make sense ?

Yes, got that. Then what?

 

[Tanya Sharma]

Solve and obtain value of I₂ .This is what you want.

 

[Allura]

Solve and obtain value of I₂ .This is what you want.

Why are we solving for I₂ though?

 

[Tanya Sharma]

Why are we solving for I₂ though?

Because this is what the question is asking .I₂ is flowing through the resistor g .