### Conversion of electrical units (Capacitance) into energy and power units

Symbols used in this notes are:

F – Faraday; C – Coulomb; V – Volt; A – Ampere; J –Joules; s – second; W – Watt; g – gram; h – hour

Correlation between electrical (capacitance) and energy and power units

F = C/V

W = A×V

C = A×s

J = W×s (Energy unit)

F = A×s/V

So, F×(V^2) = A×s×V = W×s = J

Capacitance is expressed in, F

Energy is expressed in, Wh

Power is expressed in, W

Specific Capacitance is expressed as: F/kg (or) F/g

Specific Energy is expressed as: Wh/kg (or) Wh/g

Specific Power is expressed as: W/kg (or) W/g

Assume a supercapacitor has a Specific Capacitance of 2000 F/g and discharges at a potential difference of 1 V in 900 s, then Specific Energy and Specific Power is related to its Specific Capacitance as:

Formula:

Specific energy = 0.5 × Specific Capacitance × (dV)^2

Here, Specific Capacitance = 2000 F/g and dV = 1 V

= 0.5 × 2000 F/g × (1 V)^2

= 1000 F/g V^2 = 1000 J/g

= 1000 W×s /g

= {1000 W×s /g} / 3600 = 0.2778 Wh/g

= 0.2778 Wh/g × 1000 = 277.8 Wh/kg

So, Specific Energy = 277.8 Wh/kg

Specific Power = Specific Energy / time (in hour)

Discharge time = 900 s/3600 = 0.25 h

So, Specific Power = (277.8 Wh/kg) / (0.25 h) = 1111.2 W/kg

By,

Dr. M Kanagasabapathy

Assistant Professor

Department of Chemistry

Rajapalayam Rajus’ College