L1 R1 RC L2
The capacitor model we have used so far has been
treated as an ideal circuit element. A more accurate
model for a capacitor is shown in Figure P4.67. The
ideal capacitor, C, has a large “leakage” resistance, RC,
in parallel with it. RC models the leakage current
through the capacitor. R1 and R2 represent the lead
wire resistances, and L1 and L2 represent the lead wire
inductances.
a. If C = 1 μF, RC = 100 MΩ, R1 = R2 = 1 μΩ and
L1 = L2 = 0.1 μH, find the equivalent impedance
seen at the terminals a and b as a function of
frequency ω.
b. Find the range of frequencies for which Zab is
capacitive, i.e., Xab > 10|Rab.
Hint: Assume that RC is is much greater than 1/wC so that
you can replace RC by an infinite resistance in part b.
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