Find the current and potential difference

In summary, the circuit shown in the figure can be rearranged into a series of 4Ω and 8Ω resistors, giving a total equivalent resistance of 12Ω. The current through the circuit is 2A.
  • #1
spice1510
2
0

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.
 
Physics news on Phys.org
  • #2
spice1510 said:

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.
 
  • #3
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
 
Last edited:
  • #4
spice1510 said:
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.
 
  • #5




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.
 

What is current and potential difference?

Current is the flow of electric charge per unit time, while potential difference is the difference in electric potential between two points. Essentially, current is the movement of charge, and potential difference is the driving force behind that movement.

How do you determine the current and potential difference in a circuit?

To determine the current in a circuit, you can use Ohm's law (I = V/R) where I is current, V is voltage, and R is resistance. To determine the potential difference, you can measure the voltage across two points in the circuit using a voltmeter.

What factors affect the current and potential difference in a circuit?

The current in a circuit is affected by the voltage and the resistance. A higher voltage will result in a higher current, while a higher resistance will result in a lower current. The potential difference is affected by the voltage of the power source and the resistance of the circuit components.

What is the unit of measurement for current and potential difference?

The unit for current is amperes (A) and for potential difference is volts (V). These units are named after the scientists who discovered and studied these concepts, André-Marie Ampère and Alessandro Volta.

How does the direction of current and potential difference affect a circuit?

The direction of current flow determines the direction of energy flow in a circuit. If the current is flowing in the opposite direction of the potential difference, the energy is being consumed by the circuit. If the current is flowing in the same direction as the potential difference, the energy is being supplied to the circuit by the power source.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
504
  • Introductory Physics Homework Help
Replies
3
Views
488
  • Introductory Physics Homework Help
Replies
3
Views
194
  • Introductory Physics Homework Help
Replies
30
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
871
  • Introductory Physics Homework Help
Replies
15
Views
1K
Replies
2
Views
698
  • Introductory Physics Homework Help
Replies
4
Views
2K
Back
Top