Find the current and potential difference

[spice1510]

Homework Statement

For the circuit shown in the figure, find the current through and the potential difference across each resistor.
http://session.masteringphysics.com/problemAsset/1169464/1/jfk.Figure.23.P60.jpg

Homework Equations

V=I(amps)/R(ohms) and Req=R1+R2+R3...

The Attempt at a Solution

Rearranging the circuit:
R(8ohm) and R(24ohm) are parallel so (1/8+1/24)^-1=6ohm
that created a series of R(6ohm)+R(6ohm) so R6+R6=R(12ohm)
now I have the first circuit R(4ohm) in parallel with R(12ohm) and R(24ohm)
(1/4+1/12+1/24)^-1=2.67ohm for equivalent resistance for the entire circuit

24V=I*2.67ohm
I=9Amps

across the 4ohm resistor the current is? I=9A because the current is the same or is it 9A divided across the 3 parallel resistors?

I'm either getting it wrong because I put the 4ohm by itself (before the junction correct?) or if it's in series with the 2 6ohm resistors then that's my error but I've definitely tried it 4 different ways and am getting something wrong.

 

[SammyS]

Homework Statement

For the circuit shown in the figure, find the current through and the potential difference across each resistor.
http://session.masteringphysics.com/problemAsset/1169464/1/jfk.Figure.23.P60.jpg

Homework Equations

V=I(amps)/R(ohms) and Req=R1+R2+R3...

The Attempt at a Solution

Rearranging the circuit:
R(8ohm) and R(24ohm) are parallel so (1/8+1/24)^-1=6ohm
that created a series of R(6ohm)+R(6ohm) so R6+R6=R(12ohm)
now I have the first circuit R(4ohm) in parallel with R(12ohm) and R(24ohm)

No, the 12Ω and 24Ω are in parallel. The 4V is in series with the (12V & 24V) combination.

(1/4+1/12+1/24)^-1=2.67ohm for equivalent resistance for the entire circuit

24V=I*2.67ohm
I=9Amps

across the 4ohm resistor the current is? I=9A because the current is the same or is it 9A divided across the 3 parallel resistors?

I'm either getting it wrong because I put the 4ohm by itself (before the junction correct?) or if it's in series with the 2 6ohm resistors then that's my error but I've definitely tried it 4 different ways and am getting something wrong.

Homework Statement

Homework Equations

The Attempt at a Solution

See the comment in red.

 

[spice1510]

so 4ohm in series with (1/12+1/24)^-1 which equals 8ohm

4ohm+8ohm (series)=12ohm for the entire circuit

24V=12ohm*I
I=2amps

 

[SammyS]

so 4ohm in series with (1/12+1/24)^-1 which equals 8ohm

4ohm+8ohm (series)=12ohm for the entire circuit

24V=12ohm*I
I=2amps

Yes.

Now, work your way back through all the resistors.

 

[rwisz]

The current through each resistor in a parallel circuit is the same, so the current through the 4ohm resistor would also be 9A. However, the potential difference across each resistor will be different since they have different resistances. To find the potential difference across each resistor, you can use Ohm's law (V=IR) with the current value of 9A and the resistance of each individual resistor. For example, the potential difference across the 4ohm resistor would be V=9A*4ohm=36V. Similarly, the potential difference across the 6ohm resistor would be V=9A*6ohm=54V and the potential difference across the 12ohm resistor would be V=9A*12ohm=108V. It's important to note that the potential difference across the parallel resistors will add up to the total potential difference of 24V. Therefore, you can also find the potential difference across the 24ohm resistor by subtracting the sum of the potential differences across the other resistors from the total potential difference of 24V (24V-(36V+54V+108V)=-174V). This confirms that the current and potential difference values you calculated are correct.