Determine the capacitance (in μF) required for the circuit below to achieve unity power factor correction (cos θ =1). Assume a function generator frequency of 1 kHz.

(Note: The calculated capacitance will be placed in parallel with the RLC network. Assume the 10 ohm resistor is negligible.)

DO NOT INCLUDE YOUR UNITS IN THE ANSWER AS THIS QUIZ QUESTION GRADES ONLY NUMERICAL VALUES.

POWER FACTOR is the ratio between the useful (true) power (kW) to the total (apparent) power (kVA) consumed by an item of a.c. electrical equipment or a complete electrical installation. It is a measure of how efficiently electrical power is converted into useful work output. The ideal power factor is unity, or one. Anything less than one means that extra power is required to achieve the actual task at hand.

Determine the existing power factor (no units) of the circuit shown below. Assume a function generator frequency of 1 kHz.

(Note: Assume the 10 ohm resistor is negligible.)

The phase angle between two sine waves can be determined from the Lissajous plot of these two waveforms when the oscillloscope is set to X-Y mode. The phase angle θ = sin-1(A/B) where A and B are defined in the diagram below.

Determine the phase angle (in degrees) using the Lissajous plot on the oscilloscope screen below.

DO NOT INCLUDE YOUR UNITS IN THE ANSWER AS THIS QUIZ QUESTION GRADES ONLY NUMERICAL VALUES.

The oscilloscope settings are as follows:

CH1: 5 Volts / DIV

CH2: 5 Volts / DIV

Calculate the frequency (in Hz) at which series resonance occurs for the circuit shown below. 

DO NOT INCLUDE YOUR UNITS IN THE ANSWER AS THIS QUIZ QUESTION GRADES ONLY NUMERICAL VALUES.

Match the reactance of the component with its behaviour as the source frequency is increased.

Z_C - impedance of capacitor

Z_L - impedance of inductor

Z_R - impedance of resistor

Determine the phase angle (in degrees) between the two sine waves displayed on the oscilloscope screen below.

DO NOT INCLUDE YOUR UNITS IN THE ANSWER AS THIS QUIZ QUESTION GRADES ONLY NUMERICAL VALUES.

The oscilloscope settings are as follows:

CH1: 5 Volts / DIV

CH2: 5 Volts / DIV

Time/DIV: 0.2 ms / DIV

The resonance of a series RLC circuit occurs when the inductive and capacitive reactances are equal in magnitude. These reactances therefore cancel each other because they are 180 degrees apart in phase. The cancelling of the reactances of L and C causes the RLC circuit to behave like a simple resistor of the magnitude of its R value. The circuit impedance is lowest at the resonant frequency and hence the current flow through the device is maximized at resonance. 

An aluminium plate has a hole with diameter of  at room temperature. Calculate the temperature that needs to be achieved to get a increment of  of the area of the hole. Use 5 decimals.

Question 1.2.2

What is the flag found?

Flag format: apuCTF{flag}