# Circuit With Three Batteries Two Resistors

• shannonbe
In summary, for the given circuit with V1 = 12.00 V, V2 = 6.00 V, V3 = 3.00 V, R1 = 220.0, and R3 = 270.0, using Kirchhoff's voltage law, we can find that the student's guess for the direction of current across resistors R1 and R3 is correct. The resulting equations from applying Kirchhoff's voltage law in the top and bottom loops are -I1R1+V1-V2=0 and -V2+V3-I3R3=0, respectively. Solving for I1 and I3 will give us the current across resistors R1 and
shannonbe
In the above circuit:
V1 = 12.00 V V2 = 6.00 V V3 = 3.00 V
R1 = 220.0 R3 = 270.0

Because of the direction of the batteries, a student looking at the above circuit makes this guess for the direction of current across resistors R1 and R3. Is the student right, or wrong?

Find the current across resistors R1 and R3. If the student's choice of direction is RIGHT, the sign of the respective current you enter should be POSITIVE. If the student's choice of direction is WRONG, the sign of that current should be NEGATIVE. (Don't discount the possibility that a current might be zero, either!)

Solve for I3=
I1=

(If you have trouble, this hint: Note that the central battery polarity is OPPOSITE what you would expect to make a nice, neat loop. How do you think you should handle two batteries in a loop that are hooked up with OPPOSITE, not the same, polarities?)http://www.webassign.net/userimages/qid1025007.bmp?db=v4net&id=76445

Attempt at a Solution: I know I use Kirchoff's Laws but I cannot figure out what to do with no resistor in the central wire. I know that that means infinite current but cannot determine the effect it would have on the other two.

shannonbe said:
In the above circuit:
V1 = 12.00 V V2 = 6.00 V V3 = 3.00 V
R1 = 220.0 R3 = 270.0

Because of the direction of the batteries, a student looking at the above circuit makes this guess for the direction of current across resistors R1 and R3. Is the student right, or wrong?

Find the current across resistors R1 and R3. If the student's choice of direction is RIGHT, the sign of the respective current you enter should be POSITIVE. If the student's choice of direction is WRONG, the sign of that current should be NEGATIVE. (Don't discount the possibility that a current might be zero, either!)

Solve for I3=
I1=

(If you have trouble, this hint: Note that the central battery polarity is OPPOSITE what you would expect to make a nice, neat loop. How do you think you should handle two batteries in a loop that are hooked up with OPPOSITE, not the same, polarities?)http://www.webassign.net/userimages/qid1025007.bmp?db=v4net&id=76445

Attempt at a Solution: I know I use Kirchoff's Laws but I cannot figure out what to do with no resistor in the central wire. I know that that means infinite current but cannot determine the effect it would have on the other two.

For infinite current there would have to be a path without any resistance between the terminals of a voltage source. Can you show that such a path exists for the middle battery?

What have you learned about Kirchhoff's laws?

We have learned how to apply Kirchoff's rules. I am sure that this problem is a lot easier than I am making it out to be but we have not done many examples in class.

Why don't you try to apply Kirchhoff's voltage law around one of the loops? Can you write the resulting equation?

Top Loop: starting from junction at lower left corner -I1R1+V1-V2=0

Bottom Loop: Starting from bottom right junction -V2+V3-I3R3=0
Is this correct? If so, I know how to go about solving from here.

Both look fine. Solve for I1 and I3.

## 1. How do batteries and resistors work in a circuit?

Batteries provide a source of electrical energy, while resistors limit the flow of current in a circuit. When connected in a circuit, the batteries supply the energy and the resistors control the flow of that energy.

## 2. What is the purpose of having three batteries and two resistors in a circuit?

The three batteries provide a higher voltage output, which can power more complex circuits or devices. The two resistors help regulate the flow of current and protect the circuit from damage.

## 3. What happens if one of the batteries in the circuit dies?

If one of the batteries in the circuit dies, the overall voltage output will decrease, affecting the performance of the circuit. This can also cause an imbalance in the flow of current, potentially damaging the remaining batteries and other components in the circuit.

## 4. How do you calculate the total resistance in a circuit with three batteries and two resistors?

To calculate the total resistance in a circuit, you need to know the individual resistance values of each component. In a series circuit like this one, you can simply add the resistances together to get the total resistance.

## 5. Can you add more batteries and resistors to this circuit?

Yes, you can add more batteries and resistors to this circuit. However, it is important to make sure that the total voltage output and the total resistance are within the safe operating limits of the circuit to prevent damage or malfunction.

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