= Solution
For constant current and nearly constant capacitance,
$$
I=C\frac{dV}{dt},\qquad V(t)=V(0)\pm\frac{|I|}{C}t.
$$
An ideal <supercapacitor> therefore has \b[approximately linear charge and discharge ramps], making a triangular voltage–time trace. Series resistance adds an immediate voltage step when current starts and a step of magnitude $2|I|R_s$ when it reverses directly from $+I$ to $-I$. Leakage and voltage-dependent capacitance introduce curvature.
A secondary <battery> instead follows electrode chemical potentials as its state of charge changes; many chemistries have broad plateaus or sloping plateaus, with polarization separating the charge and discharge curves. This distinction is typical rather than universal: some batteries have steeply sloping profiles, while strongly potential-dependent pseudocapacitive materials can depart substantially from a triangle.
\Image[/past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2022/paper-1-supercapacitor.png]
{title=Idealized supercapacitor and battery responses, with capacitance–potential alternatives}
{description=Original schematic curves; the lower panels distinguish a constant differential capacitance, a double-layer minimum and a localized redox contribution. They are alternative models, not a universal measured curve.}
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