Circuit with Resistors and Two Opposing EMFs

In summary: So if your answer is positive, the current direction is assumed to be correct. If it's negative, the current direction is the opposite of the assumed direction.
  • #1
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Homework Statement


The circuit shown in Fig. 25.37 contains two batteries, each with an emf and an internal resistance, and two resistors. Find (a) the current in the circuit (magnitude and direction) . . .

The circuit is a rectangle with the emfs at the top and bottom sides and the resistors on the left and right sides. The positive side of each emf is towards the left side, so that one creates a current clockwise and the other an opposing one counterclockwise. The resistances are: left, 5.0; right, 9.0; top (internal), 1.6; bottom (internal), 1.4. The emf at the top is 16 and at the bottom 8.

Homework Equations


V = IR
V = E - Ir
I = E / (r+R)

The Attempt at a Solution


For the formula I = E / (r+R), since the denominator is the sum of all the resistances, I assumed I could sum all the emfs as well (taking sign and direction into account). So I did:

I = (16-8) / (1.4+5+1.6+9) = 8/17

I do not know what the correct answer is, but I intuitively feel like this answer is wrong.
 
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  • #2
The current magnitude is correct. How is the current drawn on the circuit, is it flowing clockwise or counterclockwise?
 
  • #3
Wow, so that is the correct magnitude? That's good. The direction should be counterclockwise, since the top emf is stronger than the bottom one, and the top one is going counterclockwise.

And just for clarity I drew a rough sketch of the diagram:

PhysicsCircuit.png
 
  • #4
Yes, your magnitude and direction are correct. Just remember that when doing a KVL around a loop, if your answer is positive your assumed current direction is correct. If negative, the direction of the current is opposite of the assumed direction.


For example, say I was summing the voltages around the loop in the clockwise direction:

16V + I(9) + (-8V) + I(1.4) + I(5) + I(1.6) = 0V
I = -8/17 A

Since I assumed a clockwise direction for the current, the answer came out negative. This is telling me the current is actually going in the opposite of the assumed direction.
 

Related to Circuit with Resistors and Two Opposing EMFs

1. What is a circuit with resistors and two opposing EMFs?

A circuit with resistors and two opposing EMFs is a type of electrical circuit that has resistors, or components that resist the flow of electricity, and two opposing EMFs, or electromotive forces. This means that the circuit has two power sources that are pushing electrons in opposite directions, creating a balance between the flow of electricity.

2. How does a circuit with resistors and two opposing EMFs work?

A circuit with resistors and two opposing EMFs works by balancing the flow of electricity between the two power sources. The resistors in the circuit limit the amount of current that can flow, while the two opposing EMFs create a balance between the electrons being pushed in one direction and pulled in the other. This results in a stable flow of electricity in the circuit.

3. What are the components of a circuit with resistors and two opposing EMFs?

The components of a circuit with resistors and two opposing EMFs include resistors, two power sources (such as batteries), and connecting wires. The resistors can be in the form of physical components, such as resistors made of ceramic or metal, or they can be the natural resistance of the materials in the circuit.

4. What are some practical applications of a circuit with resistors and two opposing EMFs?

A circuit with resistors and two opposing EMFs has many practical applications. It is commonly used in electronic devices to regulate the flow of electricity and create a stable power supply. It can also be used in electrical systems to prevent overload and regulate voltage. Additionally, it is used in scientific experiments to study the behavior of electricity in circuits.

5. How can I calculate the voltage and current in a circuit with resistors and two opposing EMFs?

To calculate the voltage and current in a circuit with resistors and two opposing EMFs, you can use Ohm's Law, which states that voltage (V) is equal to the current (I) multiplied by the resistance (R). You can also use Kirchhoff's circuit laws, which state that the sum of all voltages in a closed loop is equal to zero and the sum of all currents entering and leaving a node is equal to zero.

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