Answer to Question #204524 in Electrical Engineering for A jaif

Question #204524

A voltage source 𝑣(𝑡)=240 sin(314.16𝑡−20v°)𝑉 is connected to a load having an toa load having an impedance of Z. The resulting current through the load is 𝑖(𝑡)=15 sin(314.16𝑡+22.5°)A. Determine the circuit power factor and identify the elements that constitute the load, given that Z comprises of only two elements connected in series.


1
Expert's answer
2021-06-09T04:35:03-0400

From the given values of current and voltage.

"V_{rms}=240\/\\sqrt2\\newline\nI_{rms}=15\/\\sqrt2\\newline\nPhase \\space angle= 20+22.5=42.5"


This indicates the load is a capacitive load.

Magnitude of impedance"=V_{rms}\/I_{rms}"


"Z=240\/15=16\\varOmega\\newline\nR=Zcos\\phi=16cos42.5=11.80\\varOmega\\newline\nX=Zsin\\phi=10.81\\varOmega\\newline\ni.e Z=11.8 - j10. 81"


The capacitor value ="\\frac{1}{X\\omega}=\\frac{1}{10.81\\times314.16}=0.294\\times10^{-3}F=0.294mF"


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