What is the internal resistance of the battery?

[scholio]

Homework Statement

a battery with unknown internal resistance and open circuit potential (emf) is connected toa 3 ohm external resistor. the terminal potential is found to be 60 volts. when the same battery is connected to a 48 ohm resistor, the terminal potential is 96 volts. what is the internal resistance of the battery?

Homework Equations

electric potential V = IR where I is current, R is resistance

current I = epsilon/R where epsilon is emf

The Attempt at a Solution

I_1 = V_1/R_1 = 60/3 = 20 ampere

I_2 = V_2/R_2 = 96/48 = 2 ampere

now that is as far as i got, to find R internal, do i use a similar formula to R = V/I where V and I are the change in them?

how does the emf come into play?

 

[buffordboy23]

First, your analysis about the current is wrong--you never took into account the internal resistance of the battery. In actuality, the current is I = V / (R_int + R), where R is the value of the resistor and R_int is the internal resistance of the battery. Anyways, this is the wrong approach.
The key equation is the "voltage divider" equation: V = V_bat [R/(R + R_int)]. In this case, V is the voltage, or potential difference, between a point in the circuit just above the added resistor and the ground. Now, your given two cases but there are two unknowns in each case: (1) the battery's voltage and (2) the internal resistance. Are any of these unknowns constant? If so, what can we do with our two equations obtained from both cases?
I noticed that you posted a lot of questions about circuits. If your willing to learn, and take the time, I recommend downloading a SPICE application--with it you can build circuits for most homework problems and obtain the desired quantity and check your work accordingly. Good luck!

 

[Moetasim]

To find the internal resistance of the battery, we can use the formula R = (V_1 - V_2)/(I_1 - I_2), where V_1 and V_2 are the terminal potentials and I_1 and I_2 are the corresponding currents for the two different external resistors. This formula takes into account the change in voltage and current when the external resistance is changed.

The emf of the battery is the maximum potential difference that the battery can provide when there is no external load connected. In this case, the emf is not directly used to calculate the internal resistance, but it is important to keep in mind as it is a measure of the battery's ability to generate an electric current.

In summary, to find the internal resistance of the battery, we can use the formula R = (V_1 - V_2)/(I_1 - I_2) and the emf is a measure of the battery's ability to generate an electric current.