How to Determine the EMF of a Battery Using Two Voltmeters?

[palkia]

Homework Statement

We have to measure emf of a battery. We have to voltmeters. Each of them when connected alone across the battery, they read V1 = 0.9V and V2 = 0.6V and when both of them are connected to the battery simultaneously, they both read V3 = 0.45V . What is the emf of battery

Homework Equations

E-ir=V

The Attempt at a Solution

I don't know how to proceed...I thought the voltage across the battery will be it's emf when connceted without a load but it is showing different readings for the voltmeter

 

[CWatters]

Find out the difference between an "ideal" voltmeter and a "real" voltmeter. Likewise ideal and real batteries.

 

[palkia]

ideal voltmeter-Which doesn't influence the circuit

Real voltmeter-Which has resistance that is not infinitely largeSame for battery

 

[palkia]

okay so it makes sense that it shows different readings now...but still How can I proceed if they have different resistance

 

[CWatters]

Ok so you will need to decide how many unknowns there are and give them names (eg R1 is the resistance of Voltmeter 1).

Then write some simultaneous equations and if you have enough then you can solve them.

 

[palkia]

V1=E- I1R1
V2=E-I2R2
V3=E-I3R3

It's getting bigger to solve as I tried

 

[palkia]

In the last case,when we connect the voltmeters ,my book states that I3=I1+I2 but I am not sure How it came

 

[CWatters]

V1=E- I1R1
V2=E-I2R2
V3=E-I3R3

I don't think those are correct. What about the battery resistance? With just one voltmeter connected the circuit looks like this...

So the equations would be

V1 = EMF - (I1*R_B)
you also know
I1 = V1/R1

V2 = EMF - (I2*R_B)
you also know
I2 = V2/R2

With both meters connected...

V3 = EMF - (I3*R_B)
you also know
I3 = V3/R3
and
R3 = R1 in parallel with R2