A simple and accurate technique to compute essential parameters needed for electrical characterization of photovoltaic (PV) modules is proposed. A single-diode model of PV modules, including those with series and shunt resistances, is considered accurate and simple. However, PV module datasheets provided by manufacturers provide current-voltage ($I$-$V)$ characteristics as well as the values of selected parameters at standard test conditions (STC), i.e. solar radiation of 1000 W/m$^{2}$, air temperature of 25 $^{\circ}$C, and air mass AM = 1.5. Consequently, important parameters such as series resistance ($R_{s})$, shunt resistance ($R_{sh})$, photocurrent ($I_{ph})$, and diode reverse-saturation current ($I_{o})$ are not provided by most manufacturers. Since these parameters are crucial for PV module characterization, our study presents an exact, closed-form expression for $R_{s}$ that is solvable numerically while increasing the value of the ideality factor ($a)$ in small increments, so that four equations are formulated to compute the unknown parameters. To validate the proposed approach, a set of $I-V$ curves were computed for different values of $a$, and these results were compared alongside corresponding reference data for the BP SX150 and MSX60 PV modules. Average RMS errors of 0.035 for BP SX150 and 0.014 for MSX60 between the reference data and the computed data suggest that proposed approach could be used as an alternative method to quantify important missing parameters required for characterization of PV modules.