Solution:

Calculation of Circuit Current through Each Impedance:

To calculate the circuit current through each impedance, we need to find the impedance of each component using the formulas:

Impedance of a Resistor = R
Impedance of an Inductor = jωL
Impedance of a Capacitor = 1/jωC

Where R is the resistance, L is the inductance, C is the capacitance, ω is the angular frequency (2πf), and j is the imaginary unit.

i) Impedance of Resistance:

The impedance of resistance is equal to its resistance, which is 300 ohms.

ii) Impedance of Inductor:

The impedance of an inductor is given by:

jωL = j(2πf)L = j(2π×50)(130×10^-3) = j40.84 ohms

Where f is the frequency and L is the inductance.

iii) Impedance of Capacitor:

The impedance of a capacitor is given by:

1/jωC = -j/(2πfC) = -j/(2π×50×25×10^-6) = -j127.32 ohms

Where C is the capacitance.

Now, we can calculate the total impedance of the circuit by adding the impedances of all three components in parallel.

Total Impedance = (1/R + 1/jωL + 1/jωC)^-1

= (1/300 + 1/j40.84 + 1/-j127.32)^-1

= 51.06 - j31.86 ohms

The circuit current can be calculated using Ohm's Law:

I = V/Z

Where V is the voltage and Z is the impedance.

i) Current through Resistance:

I1 = V/R = 240/300 = 0.8 A

ii) Current through Inductor:

I2 = V/ZL = 240/(51.06 - j31.86) = 3.08∠-33.8° A

iii) Current through Capacitor:

I3 = V/ZC = 240/(-j127.32) = 1.89∠90° A

Calculation of Total Power Consumption:

The total power consumption of the system can be calculated using the formula:

P = VI cos(φ)

Where V is the voltage, I is the current, and φ is the phase angle.

The total power factor can be calculated using the formula:

cos(φ) = Re{S}/|S|

Where S is the complex power and Re{S} is the real part of S.

The complex power can be calculated using the formula:

S = VI*

Where V* is the complex conjugate of V.

The total power consumption is:

P = VI cos(φ) = Re{S} = 240×(0.8 + 3.08∠-33.8° + 1.89∠90°) = 523.2 W

The total complex power is:

S = VI* = 240×(0.8 - j3.08∠33.8° + j1.89∠-90°) = 523.2 - j311.5 VA

The total power factor is:

cos(φ) = Re{