How to Calculate Current Distribution in a Circuit?

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To calculate current distribution in a circuit with resistors in parallel, the total current entering the parallel assembly is equal to the current through each resistor based on their resistance values. Given a total current of 2A and resistances of 6Ω, 3Ω, and 2Ω, the current splits in the ratio of the inverses of their resistances, resulting in a distribution of 0.33A through the 6Ω resistor, 0.66A through the 3Ω resistor, and 1A through the 2Ω resistor. To demonstrate this mathematically, one can set up a linear equation based on the current ratios derived from the resistances. Understanding both the principle and the calculations is essential for accurately showing the current distribution.
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Homework Statement



I just need help with part B, I'm pretty sure part A is useless but I found Req to be 5 ohm

http://img146.imageshack.us/img146/4499/physicsrh2.jpg


Homework Equations



V=IR

The Attempt at a Solution




Well basically I found the voltage change going through the 5ohm to be 10v but then I don't understand how to find the current through anywhere else.
 
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if the current through the 5 \Omega resistor is 2A, then the current through the assembly of the 3 resistors i.e. the assembly of the 6 \Omega, 3 \Omega and 2 \Omega is also 2A as both these assemblies are in series.

So, for the assembly of three resistors, you have the incoming current as 2A. When the current splits in more than two arms, the current in each arm is inversely proportional to current. This follows from the formula V = IR, as all three arms are in parallel, they are across the same potential difference and I becomes inversely proportional to R.

So, if the arms have resistances in ratio 1:2:3, the current in each arm will split in the ratio 3:2:1 i.e. the arm with the lowest resistance will have the highest current through it.. however the ratio still holds.

In your example, the resistances are in the ratio 6:3:2. Hence the current will be in the ratio 2:3:6. How does this divide into 2A of current? Construct a linear equation and solve for it. You shall have your answer...
 
rohanprabhu said:
if the current through the 5 \Omega resistor is 2A, then the current through the assembly of the 3 resistors i.e. the assembly of the 6 \Omega, 3 \Omega and 2 \Omega is also 2A as both these assemblies are in series.

So, for the assembly of three resistors, you have the incoming current as 2A. When the current splits in more than two arms, the current in each arm is inversely proportional to current. This follows from the formula V = IR, as all three arms are in parallel, they are across the same potential difference and I becomes inversely proportional to R.

So, if the arms have resistances in ratio 1:2:3, the current in each arm will split in the ratio 3:2:1 i.e. the arm with the lowest resistance will have the highest current through it.. however the ratio still holds.

In your example, the resistances are in the ratio 6:3:2. Hence the current will be in the ratio 2:3:6. How does this divide into 2A of current? Construct a linear equation and solve for it. You shall have your answer...


Thanks for the help, I don't really understand to show the science but basically the 6ohm resistor will get .33A, 3ohm will get .66A and the 2ohm will get 1A? How do I show that?
 
jcpwn2004 said:
Thanks for the help, I don't really understand to show the science but basically the 6ohm resistor will get .33A, 3ohm will get .66A and the 2ohm will get 1A? How do I show that?

well.. yes.. you have got it right. What exactly do you need help with showing? The principle behind this method or the mathematical solution of the answer?
 
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