How Do You Solve a Parallel Circuit Problem with Unequal Currents?

• Engineering
• Peter Ke
In summary, the problem involves finding the values of resistors R1, R2, and R3 in a parallel circuit with an equivalent resistance of 720 ohms. The currents I1, I2, and I3 are related to each other as I2 = 3I1 and I3 = 6I1. Using the parallel circuit equation, 1/RT = 1/R1 + 1/R2 + 1/R3, and Ohm's Law, I1R1 = I2R2 = I3R3, the values of R1, R2, and R3 can be determined to be 72 ohms each.
Peter Ke

Homework Statement

Resistor R1, R2, R3 are connected in parallel, have an equivalent resistance of 720(ohms). The currents are labeled I1, I2,and I3. I2 is 3x the value of I1, and I3 is 6x the value of I1. Calculate R1, R2, R3.

Homework Equations

I used the parallel circuit equation. 1/RT=1/R1+1/R2...

The Attempt at a Solution

[/B]
I tried to solve it like this...

1/720= 1/R1+1/(1/3R1)+1/(1/6R1)---> 720=R1+3R1)+6R1-----> 720= 10R1-----> R1=72 ohms.
I know I made a mistake or I have been following the wrong path. Please help I really don't understand this question. Thank You!

Peter Ke said:

Homework Statement

Resistor R1, R2, R3 are connected in parallel, have an equivalent resistance of 720(ohms). The currents are labeled I1, I2,and I3. I2 is 3x the value of I1, and I3 is 6x the value of I1. Calculate R1, R2, R3.

Homework Equations

I used the parallel circuit equation. 1/RT=1/R1+1/R2...

The Attempt at a Solution

[/B]
I tried to solve it like this...

1/720= 1/R1+1/(1/3R1)+1/(1/6R1)---> 720=R1+3R1)+6R1-----> 720= 10R1-----> R1=72 ohms.
I know I made a mistake or I have been following the wrong path. Please help I really don't understand this question. Thank You!
Can you upload a copy of the problem/schematic?

berkeman said:
Can you upload a copy of the problem/schematic?

I'm so sorry, this was a word problem that came from a classwork that the teacher gave me. There was no diagram that came with it.
I have seen one person who tried to solve it in this website ---> https://answers.yahoo.com/question/index?qid=20140911191648AArMp36
but he didn't explain it, he just showed his equation so I still didn't understand how he arrived on his answers.

If you could help, then thank you!

Peter Ke said:
1/720= 1/R1+1/(1/3R1)+1/(1/6R1)
With the same voltage across the resistors (parallel circuit), when the current is higher, is the resistance higher or lower?
Then look at the equation you generated. Does it indicate higher or lower resistances for the associated currents?

NascentOxygen
When the current is higher the resistance is lower because current and resistance are inversely proportional.
Based on what you said, my equation indicates that it has higher resistance when I simplify it.

Peter Ke said:
When the current is higher the resistance is lower because current and resistance are inversely proportional.
Based on what you said, my equation indicates that it has higher resistance when I simplify it.
Equivalent resistance of the parallel combination is less than the least of R1, R2 and R3.
Voltage across all the resistors is same since they are in parallel. Use Ohm's law to find the resistances.

Yea but the amount of voltage is not given so how do I even use Ohm's Law?

Peter Ke said:
Yea but the amount of voltage is not given so how do I even use Ohm's Law?
V=IR..
So, I1R1=I2R2=I3R3..
You know the relation amongst I1, I2 and I3.

Last edited:
Peter Ke
cnh1995 said:
V=IR..
So, I1R1=I2R2=I3R3..
You know the relation amongst I1, I2 and I3.
Thank you so much! I got it!

1. What is a parallel circuit?

A parallel circuit is an electrical circuit that has multiple paths for the flow of electric current. This means that the components in the circuit are connected in such a way that the current has more than one path to follow.

2. How is a parallel circuit different from a series circuit?

In a parallel circuit, the components are connected in parallel, meaning they are connected to the same two points on the circuit, but each component has its own path for the current to flow. In a series circuit, the components are connected in a series, meaning the current has to flow through each component in order.

3. How do I calculate the total resistance in a parallel circuit?

To calculate the total resistance in a parallel circuit, you can use the formula 1/Rt = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn, where Rt is the total resistance and R1, R2, R3, etc. are the individual resistances of each component. Alternatively, you can use the formula Rt = (R1 x R2 x R3 x ... x Rn) / (R1 + R2 + R3 + ... + Rn).

4. What happens to the total current in a parallel circuit?

In a parallel circuit, the total current is equal to the sum of the currents through each individual component. This means that the total current is divided among the different paths in the circuit.

5. How do I determine the voltage across each component in a parallel circuit?

In a parallel circuit, the voltage across each component is the same. This is because each component is connected to the same two points on the circuit. So to determine the voltage across a component, you can simply measure the voltage at any point in the circuit.

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