# How does a resistor connected in series with a voltmeter change the reading?

Let's say I have a single ideal voltage source supplying a voltage V0 and connect the terminals using a resistor of resistance R0. If a voltmeter is connected in parallel with the resistor R0, but along with it I connect a resistor of resistance R in series, how does this affect the reading of the voltmeter?

• Not clear if you are saying voltmeter is only connected across Ro, or is now connected across Ro in series with R. Which is it? Never mind, see you just edited. – Bob D Feb 2 '20 at 17:26
• Sorry for the confusion. I added a drawing which I hope should clarify what I mean – Peter Feb 2 '20 at 17:28

## Case 1: Ideal voltmeter

If the voltmeter given in the problem is ideal, then the resistance should be $$\infty$$.

Thus, you will have $$0$$ current in the branch having the voltmeter, thus we should have the result as exactly $$V_o$$

## Case 2: Realistic voltmeter

For a realistic voltmeter, we will not have an infinite resistance but rather some resistance value, let's say $$R_v$$.

Because of this we will have some current flowing through the branch having the voltmeter. Let us say that the current in this branch is $$I_v$$ and current through battery, ie, total current is $$I$$.

Now, using loop law, we can say: $$R(I-I_v)=(R_o+R_v)I_v=V_o$$ From the above equation we get, $$I_v = \frac{V_o}{R_v+R_o}$$ So, the reading of voltmeter should be, $$reading=I_vR_v\\ reading=V_o\frac{R_v}{R_v+R_o}$$ Since the factor of $$\frac{R_v}{R_v+R_o}<1$$, the reading of the voltmeter will be lesser than $$V_o$$ and will depend on the resistance of the voltmeter.

Hope this helps!

• Thank you very much for an incredibly quick and well-formulated reply! – Peter Feb 2 '20 at 17:45
• As much as I appreciate that Peter, according to the rules of stack exchange you should generally not use the comments to show appreciation, but rather upvote, read more here:stackoverflow.com/help/privileges/comment, in the when should I not comment section. Thanks a lot though😁! – FissionChips Feb 2 '20 at 17:50