Capacitance, conductance - practical case: A parallel platecapacitor has a d = 5 mm plate sep- aration, squareshaped plates with 2 cm X 2 cm dimensions and a dielectric fillingwith a permittivity of e = πeo and conductivityof σ = 10−3 S/m.
a) Determine the capacitance C = eA/d ofthe physical capacitor and express it in pFunits. Hint: pF=10−12 F
b) Determine theconductance G = σA/d of the same capacitor andexpress the corresponding resistance R = 1/G inkΩ units. Hint: kΩ =103 Ω.
The capacitor described above is now placed in a circuit shownbelow where a switch action at t = 10 s connects thecapacitor across 5 V source with 1 kΩ internal resistance:
Capacitance Conductance Practical Case A Parallel Plate Capacitor Has A D 5 Mm Plate Sep Aration Square Shaped P 1 (24.16 KiB) Viewed 52 times
c) If the capacitor described is holding Q = 1 Ccharge at time t = 0 (prior to closing the switch inthe above circuit), what will the capacitor charge beat t = 30 ns? Hints: (i) ns=10−9 s,(ii) redraw an equivalent circuit model where the physicalcapacitor is represented as a parallel combination of an idealcapacitor C from part (a) and an idealresistor R from part (b), (iii) rememberthat Q = CV and dV/dt + V/(RC) =0 in the circuit with the switch open and the capacitor isdischarging through R in series with C!
d) Determine the capacitor voltage at t = 20 s,10 s later than the switch action. Hint: how does 10 scompare to the time constant RthC in the circuitwhere Rthis the Thevenin resistance of the network seen by thecapacitor.
5 V + 1kΩ ww t 10 s = Physical Capacitor
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