Answer:
Explanation:
The half-life for the specified RC circuit can be expressed as
where [/tex]\tau = RC[/tex]
Given
The circuit has a resistance of 40 ohms, and by adding a new resistor of 48 ohms, the total resistance becomes 40 + 48 = 88 ohms.
Thus, the new half-life is
Now, divide equation 2 by 1
After substituting all values, we can calculate the revised half-life
Given Information:
Frequency = f = 60 Hz
Complex rated power = G = 100 MVA
Inertia constant = H = 8 MJ/MVA
Mechanical power = Pmech = 80 MW
Electrical power = Pelec = 50 MW
Number of poles = P = 4
No. of cycles = 10
Required Information:
(a) stored energy =?
(b) rotor acceleration =?
(c) change in torque angle =?
(c) rotor speed =?
Answer:
(a) stored energy = 800 Mj
(b) rotor acceleration = 337.46 elec deg/s²
(c) change in torque angle (in elec deg) = 6.75 elec deg
(c) change in torque angle (in rmp/s) = 28.12 rpm/s
(c) rotor speed = 1505.62 rpm
Explanation:
(a) Calculate the rotor's stored energy at synchronous speed.
The stored energy is represented as
Where G stands for complex rated power and H signifies the inertia constant of the turbo-generator.
(b) If we suddenly increase the mechanical input to 80 MW against an electrical load of 50 MW, we shall find the rotor's acceleration while ignoring mechanical and electrical losses.
The formula for rotor acceleration is given by
Where M is defined as
(c) If the acceleration derived in part (b) persists over 10 cycles, we will calculate both the change in torque angle and the rotor speed in revolutions per minute at the end of this duration.
The change in torque angle is expressed as
Where t is determined from
Consequently,
The change in torque in rpm/s is provided by
The rotor speed in rpm at the culmination of this 10-cycle period is calculated as
Where P indicates the number of poles on the turbo-generator.
Answer:
Ps=19.62N
Explanation:
A thorough explanation of the answer can be found in the attached files.
