Answer:
Explanation:
power factor in a series AC circuit (cosΘ) =[tex]\frac{R}{Z}[/tex]
R = resistance
Z = impedance of the circuit
Z²= R² + (XL - XC)²
XL = wL
from the question w is the angular frequency = 360 rad/s
360× 15× 10⁻³
= 5.4Ω
XC = [tex]\frac{1}{wc}[/tex]
= [tex]\frac{1}{360 * 3.5 * 10-6}[/tex]
= 793.65Ω
Z²= 250² + (5.4 - 793.65)²
= 62500 + (-788.25)²
62500+621338.06
Z²= 683838.0625
Z =√ 683838.0625
Z= 826. 95Ω
(a) power factor = R / Z
= 250 / 826.95
= 0.30
b) average power delivered to the entire circuit.
V = I × Z
I = [tex]\frac{V}{Z} = \frac{45}{826.95}[/tex]
I =0.054A
P = I× V
= 0.054× 45
= 2.43 W
c) average power delivered to the resistor
P = I²× R
= 0.054²× 250
= 0.729 W
average power delivered to the capacitor
P = I² ×XC
=0.054²× 793.65
= 2.31 W
average power delivered to the inductor
P = I²× XL
= 0.054²× 5.4
= 0.02W
The power factor of the circuit is 0.30
The average power delivered to the entire circuit is 2.43 W.
The average power delivered to the resistor, capacitor and to the inductor are 2.43w, 2.31w, and 0.02W respectively.
The formula for
power factor in a series AC circuit is (cosΘ) =R² + (XL - XC)²
Where,
R is the resistance
Z is impedance of the circuit
w is the angular frequency = 360 rad/s
Z²= R² + (XL - XC)²
XL = wL
w = 360 rad/s
360× 15× 10⁻³
= 5.4Ω
XC = 793.65Ω
Z²= 250² + (5.4 - 793.65)²
= 62500 + (-788.25)²
62500+621338.06
Z²= 683838.0625
Z =√ 683838.0625
Z= 826. 95Ω
The power factor = R / Z
= 250 / 826.95
= 0.30
To get the average power delivered to the entire circuit.
The formula is
V = I × Z
v potential difference or voltage
I = current
I =0.054A
but
P = I× V
where p is power
I is current=0.054A
v is voltage which is 45v
P= 0.054× 45
= 2.43 W
To get the average power delivered to the resistor
P = I²× R
where R is resistance.
= 0.054²× 250
= 0.729 W
To get the average power delivered to the capacitor.
P = I² ×XC
=0.054²× 793.65
= 2.31 W
To get average power delivered to the inductor
P = I²× XL
where xl is inductance.=5.4
= 0.054²× 5.4
= 0.02W
An electric circuit is comprises of electronic components like esistors, transistors, capacitors, inductors and diodes which are connected together by conductive wires through which electric current flow.
Therefore, The power factor of the circuit is 0.30
The average power delivered to the entire circuit is 2.43 W.
The average power delivered to the resistor, capacitor and to the resistor are 2.43w, 2.31w, and 0.02W respectively.
Learn more about circuit from the link below.
https://brainly.com/question/2969220
