We report a new method for determining the time constant of ac resistors with values around 10 kΩ using a digital impedance bridge for the comparison of two nominally equal resistors. This method involves adding a probing capacitor in parallel to one of the resistors to induce a quadratic frequency dependence in the real component of the admittance ratio between the two resistors. The magnitude of this quadratic effect is proportional to the self-capacitance of the unperturbed resistor, enabling us to determine its value and the associated time constant with an estimated standard uncertainty (k = 1) of 0.02 pF and 0.2 ns, respectively.