1. For the circuit of Figure 2 calculate the impedance of the load at a frequenc
ID: 1810329 • Letter: 1
Question
1. For the circuit of Figure 2 calculate the impedance of the load at a frequency of 1 kHz.
2. If the sine wave generator for the circuit in Figure 2 has a maximum voltage of 5 V, calculate
the voltage across the load and the voltage across the 100 ? resistor. Draw a phasor diagram
showing the generator voltage, the load voltage and the current. (The voltage across the 100
? resistor divided by 100 is the current). Using this phasor diagram determine the power
factor of the load.
3. What are the rms values of the three voltages in Step 2?
4. Calculate the apparent power, average power, reactive power and complex power for the
load in Figure 2 and show these on a power phasor diagram. Using this power phasor
diagram determine the power factor of the load.
5. Calculate the capacitance that when placed in parallel with the load, will raise the power
factor to unity.
Explanation / Answer
1)Let C1=0.1uF R1=1kohm L=0.1H R2=220 ohm and C2=1nF
Z(s)= [ [((1/C1s)+R1)||Ls]+R2 ] || (1/C2s)
now keep s=jw ; w=2(pi)1000
2)convert the input voltage from time domain to laplace domain and find the voltages across Z(s) and 100 ohms normally and then convert the induvudual output voltages into time domain again.using magnitude and phase we can draw the phasors now and can determine the power easily.
3)after converting into the time domain, [amplitude/sqrt(2)] gives the rms values of each of the 3 voltages
4)complex power is calculated directly from Z(s) where as the apparent,reactive power are found from the real and imaginary parts of Z(s) power factor of the load can be directly found from Z(s).
tan (theta)=imaginary/real; powerfactor=cos(theta)
5)now Z(s)||(1/Cs) inplace of Z(s) and following the same method above we can calculate C
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