Supercapacitor Supercapacitors have very large capacitances (typically from 0.1 to 50 F,) very long charge holding times, and small sizes, making them useful in non-battery backup power applications.

To measure its capacitance, a supercapacitor is charged to an initial voltage V0 ¼ 5.5 V. At t ¼ 0 the device undergoes a constant current discharge of iD ¼ 2 mA. At t ¼ 2500 s the voltage remaining on the capacitor is 3 V. Find the device capacitance.

Use MATLAB to solve problem.

(a) Use the capacitor’s i-v characteristic to find the current i(t) for t 0.

(b) Use the inductor’s i-v characteristic and i(t) to find vL(t)
for t 0.

(c) Use vC(t), vL(t), and KVL to find the voltage v(t) delivered to the rest of the circuit.

(d) The v(t) found in

(c) should be proportional to the i(t)
found in (a). If so, what is the equivalent resistance looking into the rest of the circuit?

(e) On the same axes, plot vC(t), vL(t), and v(t). Use a different color for each waveform. Use the plots to verify KVL for the circuit.

Transcribed Image Text:

t=0 2.5 mH i(t) 000 + + VL(t) + Rest of 25 F vc(t) v(t) the FIGURE P6-60 circuit