# Calculate Currents Through Ideal Batteries with Kirchhoff's Loop Rule

• subzero0137
In summary, Kirchhoff’s rules can be used to calculate the current through each ideal battery in the figure below. By applying Kirchoff’s loop rule, we can determine that i1=-2/3A, i2=-1/3A, and i3=-1/3A. Although the arrows on the figure suggest a certain direction for the current, the actual direction may be opposite due to the values used. This is where the sign of the calculated current comes in.
subzero0137
"Use Kirchhoff’s rules to calculate the current through each ideal battery in the figure
below. R1=1Ω, R2=2Ω, ε1=2V, ε2=ε3=4V. You should apply Kirchoff’s loop rule to the ε1-R1-R2-ε2-R1 loop, and the ε2-R2-R1-ε3-R1 loops respectively, each time starting from the negative end of the battery and assuming that the currents flow in the directions shown."

My attempt: i1=i2+i3 (using junction rule).
Left loop:
ε1-i1R1-i3R2-ε2-i1R1=0, therefore i1+i3=-1A.
Right loop:
ε2+i3R2-i2R1-ε3-i2R1=0, therefore i3=i2.

Therefore i1=-2/3A, i2=-1/3A, and i3=-1/3A. But I'm not sure if these are the final values. The question is asking for currents through each ideal battery, so do I have to change the signs of the i2 and i3?

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It says "assuming that the currents flow in the directions shown" so I would treat those directions as positive which is what you appear to have done. eg no changes needed. If that turns out to be wrong then I would argue the question is badly worded.

CWatters said:
It says "assuming that the currents flow in the directions shown" so I would treat those directions as positive which is what you appear to have done. eg no changes needed. If that turns out to be wrong then I would argue the question is badly worded.

I see. So the currents in the batteries would flow in the same directions as the currents i1, i2 and i3?

subzero0137 said:
I see. So the currents in the batteries would flow in the same directions as the currents i1, i2 and i3?
Yes, a branch current direction and magnitude is common to all series elements in that branch.

subzero0137 said:
...

Therefore, i1=-2/3A, i2=-1/3A, and i3=-1/3A. But I'm not sure if these are the final values. The question is asking for currents through each ideal battery, so do I have to change the signs of the i2 and i3?

subzero0137 said:
I see. So the currents in the batteries would flow in the same directions as the currents i1, i2 and i3?

You assumed the directions indicated in the figure.

When you assume a direction, you can't always be sure that the current will actually flow in this direction. If the current turns out to be negative, then it flows opposite the direction assumed.

That's the case here for ALL of the currents. That doesn't mean that there's anything wrong with the way the problem is set-up. It simply shows that for the particular values used, the currents flow opposite the assumed direction. This happens frequently when applying Kirchhhoff's circuit rules.

1 person
subzero0137 said:
I see. So the currents in the batteries would flow in the same directions as the currents i1, i2 and i3?

Yes, you couldn't have the current through ε1 going the opposite way to current i1.

However the current in the battery is not necessarily in the direction of the arrows on the drawing. That's where the calculated sign comes in. The arrow for I1 defines +ve to be out of the +ve terminal of the battery ε1. However you calculated I1 to be -2/3A which means current is actually flowing into the battery ε1 (eg it's being charged).

## What is Kirchhoff's Loop Rule?

Kirchhoff's Loop Rule, also known as Kirchhoff's Voltage Law, states that the sum of the voltage drops in a closed loop circuit must equal the sum of the voltage sources in that loop. This law is used to calculate the currents flowing through ideal batteries in a circuit.

## How do I calculate the currents through ideal batteries using Kirchhoff's Loop Rule?

To calculate the currents through ideal batteries using Kirchhoff's Loop Rule, you first need to determine the voltage sources and the voltage drops in the circuit. Then, use the loop rule to set up equations that represent the voltage drops and the voltage sources. Finally, solve the equations to find the currents flowing through the ideal batteries.

## What are ideal batteries?

Ideal batteries are theoretical models of batteries that have no internal resistance, meaning that all the energy supplied by the battery is delivered to the circuit. This simplifies the calculations and allows for more accurate results when using Kirchhoff's Loop Rule to calculate currents.

## Can Kirchhoff's Loop Rule be used for circuits with non-ideal batteries?

Yes, Kirchhoff's Loop Rule can still be used for circuits with non-ideal batteries. However, the calculations become more complex because the internal resistance of the battery must also be considered in the equations. This can be done by incorporating Ohm's Law into the equations.

## What is the importance of calculating currents through ideal batteries using Kirchhoff's Loop Rule?

Calculating currents through ideal batteries using Kirchhoff's Loop Rule is important because it allows for the prediction and analysis of the behavior of electrical circuits. This can be useful in designing and troubleshooting circuits, as well as understanding the flow of electricity in a system.

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