Solve Internal Resistance Homework Problem

[nokia8650]

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

 

[kamerling]

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.

 

[Moetasim]

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