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## Homework Statement

I measured a battery rated at 1.5V(ε) and get 0.9V out and want to calculate the internal resistance (r). So, I model the battery as an ideal voltage source and a resistor in parallel. I know the voltmeter has a resistance of 1kΩ (R). How do I calculate the internal resistance?

## Homework Equations

V=IR, ∑V = 0

## The Attempt at a Solution

Subtracting 1.5-0.9 gives me 0.6V, this is the voltage lost across the internal resistor, so ΔV = 0.6V = Ir

I also know that the sum of the voltages around the circuit is zero, but I'm not sure if this means there is a voltage drop across the voltmeter resistor of 0.9V and across the internal "resistor" of 0.6V or if the internal voltage drop is equal to the voltage drop across the voltmeter. But, what I have done algebraically is this:

$$\epsilon = \Delta V_I + \Delta V_{vm} = I_ir+I_{vm}R $$

This is where I get stuck, I know what ##\epsilon## is and I know what the ##\Delta V##'s are, and I know what R is, but I don't know the current for the voltmeter or the current across the internal resistor, so I'm stuck. I have tried to use Ohm's law to express the currents as ##\frac{\Delta V_{i/vm}}{r/R}## but it just ends up being circular logic and I get some form of ##R_i = R_i##.