Calculating a voltmeter reading

Question

I'd like to preface with saying that I'm quite new to this.

Given emf E = 9 V, and that both resistances are equal, R = 1 kΩ, calculate the voltmeter reading if voltmeter's internal resistance is Rv = 10 kΩ.

So far, I have calculated E * R2 / (R1 + R2) which gives me a result of 4.5V.

But, I'm not sure how to apply the internal resistance of 10k ohms. How does it affect the final result?

Answer 1

List out what you know from the problem

E = 9 V

R1 = R2 = R = 1 kΩ

Rv = 10 kΩ

It can help to redraw the circuit to make how you're thinking about it clearer.

Apply the handy two parallel resister formula

     Rv x R2   10 x 1   10
Rp = ------- = ------ = -- kΩ
     Rv + R2   10 + 1   11

The simplified circuit is now two resisters in series.

^{simulate this circuit – Schematic created using CircuitLab}

Apply the voltage division rule

         Rp            10 / 11          10 / 11       10     30
Ep = E ------- = 9 --------------- = 9 --------- = 9 ---- = ---- ~ 4.3 V
       R1 + Rp      1 + (10 / 11)       21 / 11       21      7

Ep will be what the voltmeter (V) will read. This is within 95% of what theory predicts an idealized voltmeter (∞Ω) would have measured (4.5v). Which is not bad considering the voltmeter only has 10 times the resistance of the resisters.

You can check these results in the sites handy Circuit Lab:

^{simulate this circuit}