The continuity tester is based on the well-tried μA741. which is used as a comparator that operates a buzzer at its output. The inverting (-) input is at half the supply voltage via R3 and R4. When the potential at the non-inverting (+) inputs is lower than that at the -ve input, which is the case when the resistance between the two terminals is small enough, the buzzer will be actuated.
With values of R1, R2, and P1 as specified, the sensitivity of the tester is about 1 kΩ. The circuit is set by connecting a 1 kΩ resistor between the input terminals and adjusting P1 so that the buzzer just does not sound. The sensitivity may be increased to 100 Ω by making the values of R1, R2 and P1 ten times smaller. The circuit then draws a slightly larger current (2.5 mA instead of about 2 mA).