Calculating Current in Parallel DC Circuit - Solving for I3

In summary, the conversation discusses a problem with three resistors connected in parallel across a DC voltage source. The total current through the circuit is given as 2.0A and the question asks for the current through the 12ohm resistor. The circuit splits into three paths, each with resistors of 2ohm, 6ohm, and 12ohm. The problem is solved by using Ohm's Law and finding the equivalent resistance for the three resistors, allowing the voltage to be determined and the current through the 12ohm resistor to be calculated. The conversation ends with a note about using Ohm's Law to solve the problem.
  • #1
TheMadCapBeta
I'm having trouble solving this problem:

Three resistors(parallel) across a DC voltage source...If the total current through the circuit is I = 2.0A, what is the currect through the 12ohm resistor?

The circuit runs into a junction which splits 3 ways. Along each path there's are resistors 2ohm, 6ohm, and 12ohm, respectively, and all meet again andthen flows back to the battery.


It's parallel so I breaks up into I1, I2,I3
I found two equations:

8/3V = I1(2ohm) + I2(6ohm) + I3(12ohm)
I = I1 + I2 + I3

I found the voltage by first find the equivalent resistor for R1, R2, and R3, (R = 4/3 ohm) So V = IR => V = 2(4/3) => V = 8/3V.

I need to find the current through R3, and I could if I had one more equation, but I'm stuck. I can't see any other equations by loop rule or Kirchoff's law. So, any help will be appreciated, thanks.
 
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  • #2
Originally posted by TheMadCapBeta
I'm having trouble solving this problem:

Three resistors(parallel) across a DC voltage source...If the total current through the circuit is I = 2.0A, what is the currect through the 12ohm resistor?

The circuit runs into a junction which splits 3 ways. Along each path there's are resistors 2ohm, 6ohm, and 12ohm, respectively, and all meet again andthen flows back to the battery.


It's parallel so I breaks up into I1, I2,I3
I found two equations:

8/3V = I1(2ohm) + I2(6ohm) + I3(12ohm)
I = I1 + I2 + I3

I found the voltage by first find the equivalent resistor for R1, R2, and R3, (R = 4/3 ohm) So V = IR => V = 2(4/3) => V = 8/3V.


Good start!

I need to find the current through R3, and I could if I had one more equation, but I'm stuck. I can't see any other equations by loop rule or Kirchoff's law. So, any help will be appreciated, thanks.

Two words: Ohm's Law

You know the voltage across the 12Ω resistor (it's the same as the voltage of the battery). You also know the resistance, so just use V=IR and you're home free.

edit: typo
 
  • #3
I knew I was forgetting something. Thanks.
 

1. How do I calculate the current in a parallel DC circuit?

To calculate the current in a parallel DC circuit, you can use the formula I = V/R, where I is the current in amperes, V is the voltage in volts, and R is the resistance in ohms. You will need to calculate the current for each individual branch in the circuit and then add them together to get the total current.

2. What is the difference between series and parallel circuits?

In a series circuit, the components are connected one after another, creating a single path for the current to flow. In a parallel circuit, there are multiple paths for the current to flow, with each component connected separately. This means that in a parallel circuit, the voltage across each component is the same, while in a series circuit, the voltage is divided among the components.

3. How do I solve for I3 in a parallel DC circuit?

To solve for I3, you will need to use the formula I3 = V3/R3, where I3 is the current in amperes, V3 is the voltage in volts, and R3 is the resistance in ohms of the specific branch you are trying to solve for. You can find the values for V3 and R3 by using Ohm's law and the given values for the voltage and resistance in the circuit.

4. Can I use Kirchhoff's laws to solve for I3 in a parallel DC circuit?

Yes, you can use Kirchhoff's laws to solve for I3 in a parallel DC circuit. Kirchhoff's current law states that the sum of the currents entering a junction must be equal to the sum of the currents leaving the junction. This means that you can use the total current and the currents in the other branches to solve for the current in the specific branch you are interested in (I3).

5. What happens to the total current in a parallel DC circuit if one component is removed?

If one component is removed from a parallel DC circuit, the total current will decrease because there is now less resistance in the circuit. This means that more current will flow through the remaining branches, causing an increase in the individual currents in those branches. However, the voltage across each branch will remain the same as it was before the component was removed.

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