This continuity tester is built using an operational amplifier 741, used as a comparator which command of it output a buzzer. Inverting input (-) is at a potential equal to half the supply voltage, formed by R3 and R4. When potential of noninverting input (+) is lower than the negative input, which is the case if the resistance between two terminals is small enough, buzzer is activated.
With specified values for R1, R2 and P1, sensitivity of tester is about 1 k.
Its sensitivity can be increased to 100 ohms decreasing ten times the values of R1, R2 and P1.