Sum of branch currents more than total current?

In summary, we have an impedance of 7-2jΩ and an impedance of 4+2jΩ and a current source of 97.5A connected in parallel. Using the current-divider rule, we can find the individual branch currents to be I1=39.54A and I2=64.53A. However, these currents do not add up to the current supplied by the source due to the complex nature of the currents. It is important to consider the magnitudes rather than just the angles when applying the current-divider rule.
  • #1
ViolentCorpse
190
1

Homework Statement


An impedance of 7-2jΩ and an impedance of 4+2jΩ and a current source of 97.5A are all connected in parallel. Find the individual branch currents.

Homework Equations



Current-divider rule:

I1=I*Z1/(Z1+Z2) (only have to consider the magnitudes of the impedances, not the angle)

The Attempt at a Solution



I've obtained a value of I1=39.54A and I2=64.53A. However, these currents sum up to 104.07A, whereas the current source is supplying a current of only 97.5A. Why is there a discrepancy?
 
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  • #2
For complex current I1 and I2 it's true that I1 + I2 = (97.5 + j*0) A, but it doesn't follow that |I1| + |I2| = |(97.5 + j*0)| A
 
  • #3
Oh, I see. My bad.

Thank you very much, milesyoung!
 

1. Why is the sum of branch currents more than the total current?

This is a common misconception that arises from Kirchhoff's Current Law, which states that the algebraic sum of currents entering and exiting a node is equal to zero. However, this law applies to the currents within the circuit, not the total current entering the circuit. In a circuit with multiple branches, the sum of the individual branch currents will always be equal to the total current entering the circuit.

2. Does this mean that the total current is not conserved?

No, the total current entering a circuit is always conserved. Kirchhoff's Current Law ensures that the total current entering a circuit is equal to the sum of the currents exiting the circuit. Therefore, the sum of branch currents cannot be more than the total current.

3. How does the sum of branch currents being more than the total current affect the circuit?

This can occur in a parallel circuit, where the individual branch currents combine to form the total current. Having a sum of branch currents more than the total current does not affect the circuit's functionality, as long as Kirchhoff's Current Law is satisfied.

4. Can the sum of branch currents ever be less than the total current?

Yes, in some cases, the sum of branch currents may be less than the total current, especially in series circuits. In these cases, the individual branch currents are reduced as they pass through each component in the circuit, resulting in a lower total current.

5. How can we calculate the sum of branch currents in a circuit?

The sum of branch currents can be calculated by using Kirchhoff's Current Law, where the sum of the currents entering a node is equal to the sum of the currents exiting the same node. By applying this law to each node in the circuit, we can determine the individual branch currents and their sum.

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