1.) Calculate the equivalent impedance of each of the following at 50Hz:
2.) For each network above, calculate the complex, active, reactive and apparent power if connected to a 230 V r.m.s. 50Hz AC voltage source.
3.) Calculate the current phasor I and the active power in each of the following (treating the voltage source as the reference phasor):
4.) For each of the r.m.s. phasors in the diagram below, calculate the peak value and phase angle of the corresponding waveform. Assuming the frequency is 50 Hz, write the time domain function corresponding to each phasor.
5.) For each of the r.m.s. phasors in the diagram below, calculate the peak value and phase angle of the corresponding waveform. Assuming the frequency is 50 Hz, write the time domain function corresponding to each phasor. What is the phase difference between VR and VC?
6.) Analyse the AC circuit shown below to calculate the complex value of phasor current I. What is the active power dissipated in each component?
7.) Analyse the AC circuit shown below to calculate the active power in each element.
8.) Analyse the AC circuit shown below to calculate the complex, active, reactive and apparent power. What is the peak voltage across R1?
9.) In the circuit shown below, the switch is to the left for all t < 0, but moves to the right hand position at t=0, which causes the capacitor to begin discharging.
- State the time constant,
, of the circuit (after the switch has moved to the right).
- Sketch the waveform of the capacitor voltage.
- Derive an expression for Vc(t) for all t>=0.
- At what time is the voltage equal to 6V?
10.) In the circuit shown in Question 9, modify either R2 or C so that the capacitor voltage equals 6V at t=1 second. i.e. Vc(1)=6.
11.) In the following circuit, the switch closes at t=0.
- What is the time constant,
?
- Assuming that Vc(t)=0 for t<0, write an expression for Vc(t) in terms of t, R and C.
12.) In the circuit shown in question 11, calculate an alternative capacitance value that would give Vc(t)=4V at t=10ms.
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