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Impedance of a circuit; Fendt, Combinations of resistors

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Find impedance of the circuit below. R1 = 10 &#937;, C= 100mF

E=10VAC
60Hz

https://brainmass.com/physics/kirchhoffs-voltage-law/impedance-circuit-fendt-combinations-resistors-298194

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Find impedance of the circuit below. R1 = 10 Î©, C= 100mF
IR
I IC

Solution: Reactance of the capacitor = XC = 1/jÏ‰C = 1/j(2ÐŸfC) where f = frequency = 60 Hz
Substituting values: XC = 1/j(2ÐŸx60x100x10-3) = 1/j37.7 ohm
Let equivalent impedance of the parallel combination of the resistance and capacitance be Z. Then, 1/Z = 1/R1 + 1/XC = 1/10 + j37.7 = 0.1 + j37.7 = âˆš(0.12 + 37.72)/tan-1(37.7/0.1)
1/Z = 37.7/89.85O
Z = (1/37.7)/-89.85O = 0.0265/-89.85O ohm
Impedance can also be expressed as: Z = 0.0265cos(-89.85O) + j0.0265sin(-89.85O) = 0.0000693 - j0.0265
Z â‰ˆ - j0.0265 ohm

1. Find the voltages (V1 and V2) and current (A) across the following sets of series circuits (see figure above) where the voltage source is 12 VDC.