Given the R & L series circuit in Figure 1 , calculate the total equivalent resi

Question

Given the R & L series circuit in Figure 1, calculate the total equivalent resistance, ZT , of the circuit at frequencies, f = 1 kHz, 2kHz and 3 kHz and list the numbers obtained in the Table

Figure 1 – Series RC Circuit

              

Frequency (kHz)

Reactance, XC

         ()

Total Circuit AC Impedance, ZT

Complex Notation

Magnitude

Angle

1

2

3

Table 1 – RC Circuit Calculated Impedance Values

Frequency (kHz)

IS (RMS) - (A)

Power Factor

Complex Form

Magnitude

Angle

1

2

3

Table 2 – RC Circuit Calculated Current Values

Frequency (kHz)

Reactance, XC

         ()

Total Circuit AC Impedance, ZT

Complex Notation

Magnitude

Angle

1

2

3

Explanation / Answer

First off, in rectangular form the impedance Z, looks like

R + jX

R is the resistance of circuit
X is the reactance of the circuit

for capacitors, the formula for reactance is
-j/(C) or -j/(2fC) Ohms ()

so here is the reactance at each given frequency for C = 100 nF or 100x10-9

1 kHz: -j(1.591 x 103)

2 kHz: -j(795.775)

3 kHz: -j(530.516)

R is the same regardless of frequency...so therefore:

R = 1 k

Putting everything in the same units of k

Z @ 1 kHz (Rectangular Form): 1 - j1.591 k

Z @ 2 kHz (Rectangular Form): 1 - j0.795.78 k

Z @ 3 kHz (Rectangular Form): 1 - j0.530.52 k

To get polar you need two formulas

tan-1 (X/R) =

sqrt[ R2 + X2] = Magnitude of Polar Impedance

so...

Z @ 1 kHz (Polar Form): 1.591<-90 k

Z @ 2 kHz (Rectangular Form): 0.795<-90 k

Z @ 3 kHz (Rectangular Form): 0.530.52<-90 k

So the reactance for the given

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