In this article, we present an intriguing experimental exercise that does not fall foul of improper use of instrumentation. The activity is designed as an electronics exercise where the role of the instruments in the measurement of the RC time constant is considered. Essentially, we study the accuracy and precision of a measurement of the RC time constant in a series circuit with an oscilloscope as a function of the value of the resistor, against the predicted linear model of [tau] = RC. As the value of the resistor approaches the value of the impedance of the oscilloscope, the time constant deviates from the linear model. We show how to adapt the model to account for this and create a mathematical model that agrees with the measurements. It is hoped that such an exercise will solidify a rule of effective use of oscilloscopes--that the resistance of the circuit should be much lower than the impedance of the scope--in the mind of the student.