Question

Design a simple ohmmeter and explain the conditions of the ohmmeter circuit when the terminal to which the unknown resistance is connected "open" and "close".

Answer 1

A simple ohmmeter can be made of 2 constant resistors, 1 variable resistor, a voltage source, and a galvanometer, or a voltmeter. One puts the unknown resistance to x, and adjusts the variable resistor 2 so that the current through the galvanometer is 0 or the voltage between the terminals of the Wheatstone bridge. As soon as 0 is obtained, find the unknown resistance:

$$R_x=\frac{R_3R_2}{R_1}.$$

If the terminals where the x is supposed to be are opened, the ammeter's readings are

$$I_G=\frac{ER_1}{R_1R_2+R_2R_3+R_1R_3.}$$

If $I_G=0,$ you should record the value of $R_2$ and calculate the unknown resistance according to the first equation.

If there is a voltmeter instead of G, its readings would be

$$V_G=\frac{ER_1}{R_1+R_2}.$$

If $V_G=0,$ you should record the value of $R_2$ ​and calculate the unknown resistance.

Any other readings of $I_G, V_G$ mean that the Wheatstone's bridge is unbalanced, and the terminals of $R_x$ are closed.