Question

I just need f, g, and h.

Consider the circuit below, where R-5000Ω ,C-0.25μF . The voltage amplitude is 10 V and the frequency of oscillation is ω-180 rad / s , when voltages and currents are requested, express them in purely real terms. Note: this circuit is examined in some detail in Chapter 7, section 2. Have a look at that first. What is the total impedance? Express it as both a complex number and as magnitude and phase. What is the current in the circuit? What is the maximum current in the circuit? What is the voltage across the resistor? This will involve a phase angle. What is the phase angle with respect to? What is the current through the resistor? This will involve a phase angle. What is the phase angle with respect to? What is the voltage across the capacitor? This will involve a phase angle. What is the phase angle with respect to? If you compare the magnitudes of the voltages across the capacitor and the resistor you will see that they do not add up to 10 V. However, by making a plot of the voltages over say a 1/10 th of a second, show that at any instant the voltages do indeed add up to 10 V The voltage across the resistor is not in phase with the voltage of the source. Why is it not? What is the average power dissipated by this circuit? What would be the average power dissipated if there were no capacitor in the circuit? a) b) c) d) e) f) g) h) i)

Answer 1

Ans:

f) Xc = 1/wc = 22222.22 (-90⁰) Ω

Z = (R² + Xc²)^1/2 = 22777.77 (-77.319⁰)

φ = tan^-1(Xc/R) = 77.319⁰

I = V/Z = 0.439 (77.319⁰) mA

Voltage across capacitor = V = I * Xc = (0.439 (77.319⁰) * 22222.22 (-90⁰))

                                                            = 9.756 (-12.681⁰) Volts

g) Voltage across resister = 2.195 (77.319⁰) Volts (not getting this question exactly)

h) Vc lags current because it takes time for the capacitor to charge/discharge and Cap voltage to change.

-the current in the capacitor leads the source voltage, and the voltage across the resistor is exactly in phase with the current. Since the resistor and capacitor are in series, the current through both is exactly the same.