Question

07: How does the location of the current peak compare to the location of the voltage peak in each plot at 100 Hz? -101,186 V 271 735 ms 105.232 V capacitor, 2 F 132239 V resistor 1 169 V A/C source Figure 3 Screen capture of graphs in simulator for frequency of 100 Hz >Q8: Why does the resistor voltage increase as impedance decreases? >Q9: Which plot in Figure 1 best describes the impedance for an inductor? Q10: How does the location of the current peak compare to the location of the voltage peak in each plot at 10 Hz? Calculated XL Calculated z Measured Measured Measured z Frequency (Hz) 10 25 40 55 70 85 100 125.66 314.15 502.65 691.15 879.64 1068.1 1256.6 160.59 329.68 512.50 698.346 885.31 1072.7 1260.6 12.468 29.972 44.911 56.857 66.048 73.001 78.248 99.22 95.403 89.348 82.264 75.085 68.344 62.268 Resistor Inductor 100.78 104.82 111.92 121.56 133.18 146.32 160.59 10002 200mH Supply voltage 100V Q11: How does the location of the current peak compare to the location of the voltage peak in each plot at 100 Hz? 78 243 V inductor 69 351 V resistor 1000 100 V A/C SOURCE WMc Wm Figure 4 Screen capture of current & voltage plots in simulator with frequency at 100 Hz | >>012: What are the differences between the capacitor and inductor in an AC circuit?

I need help with Q8 and Q12, the graphs and tables are for context.

Answer 1

Q8: We have to verify why the resistor voltage increases as impedance decreases.

Let us take a impedance Z which is a series combination of resistance R and inductance L.

Hence we can write Z = R + jX_L

Where jX_L is the reactance of the inductor L and X_L = 2$\pi$fL (f is the frequency of the input AC signal)

Let the voltage across the inductor is V_l , the voltage across the resistor is V_r .

Now, as we go on increasing the frequency f , the inductive reactance X_L will increase and hence the voltage across the inductor V_l will also increase. But at that time if the resistor value R is decreased, then the voltage across the resistor V_r will decrease. Because as we assume a series circuit, we should have,

V_r = I $\times$ R and

V_l = I $\times$ jX_L      (I is the current in the series circuit)

Let us look at the table shown. (2nd row)

At f = 25 Hz, X_L = 314.15 $\Omega$ , Z = 329.68 $\Omega$ , V_l = 29.972 Volt and V_r = 95.403 Volt

In this case, R = 329.68 - 314.15 = 15.53 $\Omega$

So, at Z = 329.68 $\Omega$ , R = 15.53 $\Omega$ , resistor voltage V_r = 95.403 Volt

Similarly if we look at the 1st row, then

R = 160.59 - 125.66 = 34.93 $\Omega$

So, at Z = 160.59 $\Omega$ , R = 34.93 $\Omega$ , resistor voltage V_r = 99.22 Volt

Hence it is very much clear from 2nd row and 1st row that as the impedance Z decreases, resistor voltage V_r increases because of the increase in the value of R.

If we go on comparing the other rows, we can arrive at the same conclusion.

Q12. What are the differences between the capacitor and inductor in an AC circuit ?

Capacitor in an AC circuit - The capacitive reactance is denoted as X_C and it is defined as,

X_C = (1/2$\pi$fC) , where C is the capacitance of the capacitor and f is the frequency of the input AC signal.

If we go on increasing the frequency of input AC signal, the capacitive reactance X_C will decrease.

At zero frequency, the capacitor will behave as an open circuit because X_C will be infinite at f = 0 Hz

At infinite frequency, the capacitor will behave as a short circuit because X_C will be zero at f = Hz

OX

If a resistance R and a capacitor C are connected in series then the equivalent impedance will be

Z = R - jX_C

Inductor in an AC circuit - The inductive reactance is denoted as X_L and it is defined as,

X_L = 2$\pi$fL , where L is the inductance of the inductor and f is the frequency of the input AC signal.

At zero frequency, the inductor will behave as a short circuit because X_L will be zero at f = 0 Hz

At infinite frequency, the inductor will behave as an open circuit because X_L will be
OX
at f =
OX
Hz

If a resistance R and a inductor L are connected in series then the equivalent impedance will be

Z = R + jX_L