Answer:
(a) Z = 48.3 Ω
(b) cos ∅ = 0.455
(c) Irms = 10.35 A
(d) C = 74.02 μF
(e) Irms = 4.44 A
Explanation:
Power (P) = 2.36 kW
Frequency (f) = 50 Hz
RMS Voltage (Vrms) = 500 V
Resistance (R) = 22 Ω
Inductive Reactance (XL) = 43 Ω
(a) to calculate the total impedance, use the formula:
Z = √(R² + XL²)
= √((22)² + (43)²)
= √2333
Z = 48.3 Ω
(b) To calculate the plant's power factor, we will use the formula:
cos ∅ = R/Z
= 22/48.3
cos ∅ = 0.455
(c) To calculate the RMS current used by the plant, divide the RMS voltage value by the impedance of the plant.
Irms = Vrms/Z
= 500/48.3
Irms = 10.35 A
(d) For the power factor to become unity, the inductive reactance must be equal to the capacitive reactance i.e. Xc = XL
Xc = XL
1/(2πfC) = XL
1/(2πfXL) = C
C = 1/(2π*50*43)
= 7.402 x 10⁻⁵
C = 74.02 μF
(e) P = Vrms*Irms*cos∅
Irms = P/Vrms*cos∅
= 2.22 x 10³/500*1
Irms = 4.44 A
The value of cos θ in the given figure is 0.98.
<h3>
What is cosine of an angle?</h3>
The cosine of an angle is defined as the sine of the complementary angle.
The complementary angle equals the given angle subtracted from a right angle, 90.
cos θ = sin(90 - θ)
For example, if the angle is 30°, then its complement is 60°
cos 30 = sin(90 - 30)
cos 30 = sin 60
0.866 = 0.866
<h3>Cosine of an angle with respect to sides of a right triangle</h3>
cos θ = adjacent side / hypotenuse side
adjacent side of the given right triangle is calculated as follows;
adj² = 10² - 2²
adj² = 100 - 4
adj² = 96
adj = √96
adj = 9.8
cos θ = 9.8/10
cos θ = 0.98
Thus, the value of cos θ in the given figure is 0.98.
Learn more about cosine of angles here: brainly.com/question/23720007
#SPJ1
Answer:
7.35 J
Im assuming, upon answering the question, that the gravity in this scenario is 9.8? As 9.8 is the gravitational force upon the earth.
Answer:
R = 715.4 N
L = 166.6 N
Explanation:
ASSUME the painter is standing right of center
Let L be the left rope tension
Let R be the right rope tension
Sum moments about the left end to zero. Assume CCW moment is positive
R[5] - 20(9.8)[5/2] - 70(9.8)[5/2 + 2] = 0
R = 715.4 N
Sum moments about the right end to zero
20(9.8)[5/2] + 70(9.8)[5/2 - 2] - L[5] = 0
L = 166.6 N
We can verify by summing vertical forces
116.6 + 715.4 - (70 + 20)(9.8) ?=? 0
0 = 0 checks
If the assumption about which side of center the paint stood is incorrect, the only difference would be the values of L and R would be swapped.
350kg because to get Newton’s it’s mass x Gravity, earths gravity is x10 so 3500 divided by 10 is 350
