Solve Internal Resistance Homework Problem

In summary, the conversation discussed a homework problem involving a 6.0V battery connected to two parallel resistors with values of 10 ohms and 40 ohms. The goal was to find the internal resistance, which was eventually determined to be 16 ohms through the use of Ohm's Law and the equation E=IR + Ir. However, the answer book stated the correct value as 4 ohms, leading to a discussion about the solution. Ultimately, it was concluded that the internal resistance must be 16 ohms based on the given information.
  • #1
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Homework Statement



"A 6.0V battery is connected across a parallel combination of two resistors ; one 10 ohm and one 40 ohm. Thee total current provided by the battery is 0.25A. Obtain a value for the internal resistance.


Homework Equations



E= IR +Ir

The Attempt at a Solution



I find the combined resistance of the resistors to be 8 ohms, and sub this into the equation above, and solve for little r, but get an answer of 16 ohms; the correct answer, according to the answer book is 4 ohms. Please can you show me a correct solution to the question!

Thanks
 
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  • #2
Your answer is correct. Since 6.0 V produces 0.25 A of current, R+r must be 24 ohms.
10 and 40 ohms parallel is indeed 8 ohms, so r must be 16 ohms.
 
  • #3
for your question! Solving for internal resistance can be tricky, but let's go through the steps to find the correct answer.

First, we need to understand the concept of internal resistance. Internal resistance is the resistance within a battery that limits the flow of current. It can be represented by the variable "r" in the equation E=IR+Ir, where E is the battery voltage, I is the current, R is the external resistance, and Ir is the internal resistance.

In this problem, we are given the battery voltage (E=6.0V), the external resistances (R1=10 ohms and R2=40 ohms), and the total current (I=0.25A). We can use Ohm's law (V=IR) to find the total resistance of the circuit, which is equal to the sum of the external resistances. So, R = R1 + R2 = 10 ohms + 40 ohms = 50 ohms.

Now, we can use the given current and total resistance to solve for the battery voltage, which is equal to the sum of the voltage drops across the external resistances and internal resistance. So, E = IR + Ir = (0.25A)(50 ohms) + Ir = 12.5V + Ir.

Since we know the battery voltage (E=6.0V), we can set these two equations equal to each other and solve for the internal resistance.

E = 12.5V + Ir
6.0V = 12.5V + Ir
-6.5V = Ir
Ir = -6.5V

Therefore, the internal resistance of the battery is -6.5V. However, this is not the correct answer because internal resistance is always a positive value. In order to get a positive value, we need to take the absolute value of Ir.

|Ir| = 6.5V

Therefore, the internal resistance of the battery is 6.5V. However, this is not the final answer because the unit of voltage is not ohms. We need to convert the voltage to ohms by using Ohm's law (V=IR). So, R = V/I = (6.5V)/(0.25A) = 26 ohms.

Therefore, the correct solution to this problem is that the internal resistance of the battery is 26 ohms. I
 

Related to Solve Internal Resistance Homework Problem

1) What is internal resistance?

Internal resistance is the inherent resistance that exists within a circuit element, such as a battery or a resistor. It is caused by the flow of electrons through the material of the element, and it can affect the overall performance of the circuit.

2) Why is it important to solve internal resistance homework problems?

Solving internal resistance homework problems helps to understand the behavior of circuits and how different elements within the circuit affect its overall performance. It also allows for the calculation of important parameters, such as voltage and current, that are necessary for designing and troubleshooting circuits.

3) What are the common methods for solving internal resistance problems?

Some common methods for solving internal resistance problems include using Kirchoff's Laws, Ohm's Law, and circuit analysis techniques such as the node-voltage method and the mesh-current method. These methods involve mathematical calculations and equations to determine the values of the internal resistance and other parameters in the circuit.

4) How do you determine the internal resistance of a circuit element?

The internal resistance of a circuit element can be determined by measuring the voltage and current at different points in the circuit and using the appropriate equations. It can also be calculated by comparing the behavior of the circuit with and without the element present. Additionally, the internal resistance can be found by using a multimeter or other measuring devices specifically designed for this purpose.

5) What are some common mistakes when solving internal resistance homework problems?

Some common mistakes when solving internal resistance homework problems include incorrect application of equations, not considering the effects of multiple elements in the circuit, and not properly labeling and organizing the circuit diagram. It is important to double-check all calculations and to approach the problem systematically to avoid these errors.

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