Answer:
I = 26.36 cosω t A
Explanation:
Given that
C=0.74 mF
Vrms= 82 V
Frequency ,f= 49 Hz
We know that ω = 2 π f
ω = 2 x π x 49
ω = 307.72 rad/s
As we know that voltage given as
V= Vo sinω t

\
Vo=115.96 V
V=115.96 sinω t
The current given as




I = 26362.67 cosω t mA
I = 26.36 cosω t A
This is the current at time ant time t.
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
Answer:
Explanation:
To find the amplitude of the sound, we must first determine the wavelength and the phase difference between the two speakers.
For the wavelength;
Recall that, the separation between two successive max. and min. intensity points are 
Thus; for both speakers; the wavelength of the sound is:


λ = 80 cm
The relation between the path difference(Δx) and the phase difference(Δ∅) is:

where;
Δx = 10 cm
λ = 80 cm
Δ∅ = π rad
∴







Suppose both speakers are placed side-by-side, then the path difference between the two speakers is: Δx = 0 cm
Thus, we have:



∴
The amplitude of the sound wave if the two speakers are placed side-by-side is:



A = 0.765a
<span>Answer:
Correct answer is
just add the two kinetic energies;
E = (1/2)mv^2 + (1/2)mv^2</span>
Answer:
his acceleration rate is -0.00186 m/s²
Explanation:
Given;
initial position of the car, x₀ = 100 miles = 160, 900 m ( 1 mile = 1609 m)
time of motion, t₀ = 60 minutes = 60 mins x 60 s = 3,600 s
final position of the car, x₁ = 150 miles = 241,350 m
time of motion, t₁ = 100 minutes = 100 mins x 60 s = 6,000 s
The initial velocity is calculated as;
u = 160, 900 m / 3,600 s
u = 44.694 m/s
The final velocity is calculated as;
v = 241,350 m / 6,000 s
v = 40.225 m/s
The acceleration is calculated as;

Therefore, his acceleration rate is -0.00186 m/s²