Circuit with Two Batteries and Six Resistors

In summary, a circuit with six resistors and two batteries has been constructed. The battery voltages are V1 = 18.0 V and V2 = 12.0 V, with positive terminals indicated by a + sign. The resistors have values of R1 = R5 = 64.0 Ω, R2 = R6 = 157.0 Ω, R3 = 53.0 Ω, and R4 = 65.0 Ω. The positive directions for the currents I1, I2, and I3 are indicated by the direction of the arrows. The equations used to solve the circuit are KCL and KVL, with
  • #1
Gee Wiz
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0

Homework Statement


A circuit is constructed with six resistors and two batteries as shown. The battery voltages are V1 = 18.0 V and V2 = 12.0 V. The positive terminals are indicated with a + sign, The values for the resistors are: R1 = R5 = 64.0 Ω, R2 = R6 = 157.0 Ω R3 = 53.0 Ω, and R4 = 65.0 Ω. The positive directions for the currents I1, I2 and I3 are indicated by the directions of the arrows.

https://www.smartphysics.com/Content/Media/Images/EM/10/h10_twoloop.png

Homework Equations



KCL and KVL

The Attempt at a Solution



So i tried to make equations, but I'm not getting it to work out.
I1+I3=I2
64I1=53I3+18
 
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  • #2
It doesn't look like you have tried to simplify the circuit first?

You could replace R2+R6 with an R7.

18+53I3+157I2=12+R6I6

Personally I think it's better to write the equation so the voltages sum to zero. I haven't checked if your equation is correct but I note that I6 = I2
 
  • #3
I summed them to zero initially, and then i moved them around so there weren't any negative signs. I also saw that I6=I2. I tried playing with that using I1+I3=I2 and I6+Iv(just assigned this to the v2)=I5(which i already solved from an earlier part)
 
  • #4
nvm, just figured it out
 
  • #5
thank you!
 
  • #6
are your origional equations correct?
 
  • #7
nah, i messed up one of the loops.
 

1. How do I calculate the total resistance in a circuit with two batteries and six resistors?

The total resistance in a circuit with two batteries and six resistors can be calculated by using the formula Rtotal = R1 + R2 + R3 + R4 + R5 + R6 + Rinternal, where R1 through R6 are the resistances of each individual resistor and Rinternal is the internal resistance of the batteries. This formula applies for both series and parallel circuits.

2. What is the difference between series and parallel circuits?

In a series circuit, all components are connected in a single loop, meaning the current flows through each component in succession. In a parallel circuit, the components are connected in multiple branches, meaning the current is divided and flows through each branch simultaneously. This results in different voltage and current readings for each type of circuit.

3. How do I determine the voltage across each resistor in a circuit with two batteries and six resistors?

To determine the voltage across each resistor, you can use Ohm's law: V = IR, where V is voltage, I is current, and R is resistance. In a series circuit, the total voltage of the batteries is divided among the resistors, so the voltage across each resistor is directly proportional to its resistance. In a parallel circuit, the voltage across each resistor is equal to the total voltage of the batteries.

4. What happens to the total resistance in a circuit if a resistor is added in series or parallel?

In a series circuit, the total resistance increases when a resistor is added because the current has to flow through one more component. In a parallel circuit, the total resistance decreases when a resistor is added because the current is divided among more branches.

5. How do I calculate the current in a specific resistor in a circuit with two batteries and six resistors?

The current in a specific resistor can be calculated by using Ohm's law: I = V/R, where I is current, V is voltage, and R is resistance. For a series circuit, the current is the same throughout the entire circuit, so the current in a specific resistor is equal to the total current. For a parallel circuit, the current in a specific resistor can be calculated by dividing the total voltage by the resistance of that specific resistor.

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