As discussed in class, the RMS value of the voltage v(t) with a period T is: V rms = 1 T += Prove that Vrms =if v(t)=V, cos(at) to+I [ [v(t)]² dt

A 186-V/120-Hz source is connected to an inductance L = 0.4 H and a capacitance C = 9 μF, the elements are connected in series. Find the rms current in the circuit. The current, I =  Units             . Find the rms current through the each element in the circuit if the elements are connected in parallel. The current through L, IL =  Units             . The current through C, IC =  Units             . The current through the power source, IV =  Units

a) Write down the expression of instantaneous voltage for an AC voltage having a Peak value of 220 Volts and a frequency of 50 Hz provided at time t=0, the instantaneous voltage is 220 Volts. What is the instantaneous voltage of the source at time “t = 5 seconds” What is its RMS voltage? b) Two 200Ω resistances are connected in series with one 0.5 H Inductance and two 100μF Capacitance with the power supply of part (a). (i)Draw the circuit diagram of the above network (ii)What is the total impedance of the circuit (iii)What is the max current that flows through the Inductance? (iv)What is the max current that flows through each of the Capacitance? (v)What is the power dissipated in the circuit (vi)What is the power factor of the circuit (vii)What is the resonance frequency of the circuit? (viii) What is the maximum power dissipated by the circuit when it is in resonance

Problem #7) Specify whether each of the statements are TRUE or FALSE. D Reactive Power is a measure of the average power consumed by reactive (capacitive and inductive) loads. When connected to an AC voltage source, the instantaneous power (rate of energy transfer) supplied to a resistor varies at a frequency that is 2x the frequency of the applied source voltage. The magnitude of the impedance of a capacitor supplied by an AC source will increase as the source frequency increases. An AC source that has an RMS magnitude of 100V will supply the same average power to a resistor compared to a 100V DC source. The voltage across a capacitor is proportional to the rate of change of the current flowing through the capacitor. The magnitude of the impedance of a resistor supplied by an AC source does not vary as the source frequency increases. A complex impedance Z=R+jX, that has non-zero resistive and reactive components, will consume both real and reactive power when supplied by an AC source.…

2. What is the value of a sinusoidal voltage at 5 us (micro second) from the positive going zero crossing when V, = 20V and f = 50KHZ ? %3D 3. A sinusoidal voltage is applied to the circuit below. Determine the following: Ip, Ims, lavg, Ipp-

.......rms value..

What impedance vector (0- j15) Ohms represents:A. A pure resistance.         C. A pure capacitance.B. A pure inductance.       D. An inductance combined with a capacitance.

A complex voltage waveform which has an rms value of 240V contains 30% third harmonic and 10% fifth harmonic, both of the harmonics being initially in phase with each other. (a) Determine the rms value of the fundamental and each harmonic. (b)Write down an expression to represent the complex voltage waveform if the frequency of the fundamental is 31.83 Hz.

b) Two circuits connected in series which voltage drop across at each circuit can be expressed in time TTM domain as V1 (t) =5 sin (3147) V and V2 (1) =15 sin (314t - 30°) V. Sketch the waveforms of these voltages to illustrate peak values and phase relationships. UTM 5 UTM UTM TM S UTM UTM TM 5 UTM 8 UTM

For the circuit shown below, determine: Amplitude of the Voltage Source RMS value of the Voltage Source Frequency of the Voltage Source Phase Angle of the Voltage Source Total Resistance Total Inductance Total Capacitance Inductive Reactance Capacitive Reactance Total Impedance in Polar Form Total Current in Polar Form Voltage across the Resistor Voltage across the Inductance Voltage across the Capacitor Draw all voltages and current on the Complex Plane   show all the work