A comprehensive study for generation and design of grounded-capacitor variable-frequency RC-active oscillators using operational amplifiers (OAs) is reported. All the circuits derived are canonic, that is, the number of components (active as well as passive) in them is a minimum. First, a set of eight canonic circuits is found, each using one OA, two capacitors and six resistors. However, these circuits suffer from either a poor start-up property or a limited frequency range of variation. Thus, based on this set of eight circuits, another set of 12 variable-frequency oscillators is derived. This set provides easy tunability and a wider tuning range. Both the sets are shown to be complete. All the variable-frequency oscillators are single resistor controlled. Two of the circuits have their variable resistors grounded which makes them attractive candidates for voltage-controlled oscillators. Design equations for all the oscillator circuits are given. All the circuits have been laboratory tested. Experimental results are found to be in close agreement with the theoretical analysis. Representative test results are included in the article.