The internal resistance of supercapacitors

In this paper we study the transient behaviour of RC circuits with supercapacitors, varying R between 1 and 100 . We demonstrate that supercapacitors behave as ideal capacitors in series with an internal resistance (r ∼ 8 for C = 0.2 F, 5.5 V). This result is important to optimize the demonstration of RC circuits using a supercapacitor in series with a light bulb, because the r value is comparable with the effective resistance of the bulb. This means that the bulb brightness is significantly decreased by r . Circuits using bulbs have been used as a qualitative indicator of electric current in the teaching of DC circuits [1]. These kinds of experiments are interesting for pedagogical research [2, 3] as well as teaching using enquiry based methods [4–7]. They are particularly useful for demonstrations, since the variation of bulb brightness can be noticed by a student sitting in a classroom. More recently, low cost capacitors with high capacitance ( 0.1 F), so-called supercapacitors or ultracapacitors, have become available, enabling interesting applications in physics teaching [8]. Due to their very high capacitance, it is possible to observe the process of charging or discharging a capacitor using a bulb by observing the variation of its brightness, which takes tens of seconds. As shown in figure 1, this process is slow enough to be observed in qualitative experiments or demonstrations, which are ideal for enquirybased methods. In a recent publication the problem of (dis)charging a capacitor through a bulb was quantitatively analysed, taking into account the resistance variation of the filament due to the temperature change [9]. From a qualitative point of view, the bulb can be considered as a quasi-resistor, and the transient behaviour of the supercapacitor–bulb circuit is similar to an RC circuit, as shown in figure 1. However, the transient behaviour of a supercapacitor in an RC circuit differs from the usual due to the capacitor voltage jump at t = 0, which can be observed in both the circuit with a bulb (figure 1) or with a regular resistor, R = 8 , as shown figure 2. A supercapacitor can behave very differently from an ideal capacitor, even in a qualitative experiment. For instance, the initial brightness of the bulb in the RC circuit at t = 0 should be the same as for a circuit without the capacitor, since the initial current would be I0 = ε/R. However, in a circuit with a supercapacitor the bulb is usually much dimmer. In order to investigate this problem, we measured the (dis)charge curve of a supercapacitor (supercapacitor 0.22 F, NEC/Tokin Series FS 5.5 V) as a function of the resistor value, varying R from 1 to 100 . We analysed the magnitude of the voltage jump, V , as well as the exponential response time, τ , and showed that all data could be modelled considering the supercapacitor as an ideal capacitor, with capacitance C , in series with an internal resistance, r . We obtained the values of C and r from the analysis of the t dependence with 0031-9120/12/040439+05$33.00 © 2012 IOP Publishing Ltd P H Y S I C S E D U C A T I O N 47 (4) 439