How does the voltmeter measure the resistance of the component to measure? This is a very newbie question I guess, but I really did not find any answer on the internet that satisfies me, so here I am.
I know that to measure voltage, we use $V=I \cdot R$
How does the voltmeter calculate the resistance to use in the equation?
 A: This answer is for the working mechanism of an analog voltmeter. 
Generally a voltmeter has a tiny resistor of known resistance inside it. Thus when it is connected to a circuit with some potential difference across two points, it draws a (tiny) current. If we measure this current ($I$), we can calculate voltage using $V=IR$.
But now the question is how to measure current? For this they make an ingenious device that uses the fact the current creates a magnetic field. The device contains a coil of wire (connected to the tiny resistor) kept in between two poles of a magnet. When a current is passed in the coil, there will be repulsion between the generated magnetic field and the already present one. If the coil is light enough it can get deflected. And the deflection would be related to the strength of the generated magnetic field which is directly proportional to the current. 
 
This device is called a moving coil galvanometer. This device can be used to measure both the current and the voltage depending on how the scale of deflection is calibrated. 
