Given:
Inductance, L = 150 mH
Capacitance, C = 5.00 mF
= 240 V
frequency, f = 50Hz
= 100 mA
Solution:
To calculate the parameters of the given circuit series RLC circuit:
angular frequency,
= ![2\pi f = 2\pi \times50 = 100\pi](https://tex.z-dn.net/?f=2%5Cpi%20f%20%3D%202%5Cpi%20%5Ctimes50%20%3D%20100%5Cpi%20)
a). Inductive reactance,
is given by:
![\X_{L} = \omega L = 100\pi \times 150\times 10^{-3} = 47.12\Omega](https://tex.z-dn.net/?f=%5CX_%7BL%7D%20%3D%20%5Comega%20L%20%3D%20100%5Cpi%20%5Ctimes%20150%5Ctimes%2010%5E%7B-3%7D%20%3D%2047.12%5COmega%20)
b). The capacitive reactance,
is given by:
![X_{C} = 0.636\Omega](https://tex.z-dn.net/?f=X_%7BC%7D%20%3D%200.636%5COmega)
c). Impedance, Z = ![\frac{\Delta V_{max}}{I_{max}} = \frac{240}{100\times 10^{-3}} = 2400\Omega](https://tex.z-dn.net/?f=%5Cfrac%7B%5CDelta%20V_%7Bmax%7D%7D%7BI_%7Bmax%7D%7D%20%3D%20%5Cfrac%7B240%7D%7B100%5Ctimes%2010%5E%7B-3%7D%7D%20%3D%202400%5COmega%20)
![Z = 2400\Omega](https://tex.z-dn.net/?f=Z%20%3D%202400%5COmega)
d). Resistance, R is given by:
![2400^{2} = R^{2} + (47.12 - 0.636)^{2}](https://tex.z-dn.net/?f=2400%5E%7B2%7D%20%3D%20R%5E%7B2%7D%20%2B%20%2847.12%20-%200.636%29%5E%7B2%7D)
![R = \sqrt {5757839.238}](https://tex.z-dn.net/?f=R%20%3D%20%5Csqrt%20%7B5757839.238%7D)
![R = 2399.5\Omega](https://tex.z-dn.net/?f=R%20%3D%202399.5%5COmega)
e). Phase angle between current and the generator voltage is given by:
![tan\phi = \frac{X_{L} - X_{C}}{R}](https://tex.z-dn.net/?f=tan%5Cphi%20%3D%20%5Cfrac%7BX_%7BL%7D%20-%20X_%7BC%7D%7D%7BR%7D)
![\phi =tan^{-1}( \frac{X_{L} - X_{C}}{R})](https://tex.z-dn.net/?f=%5Cphi%20%3Dtan%5E%7B-1%7D%28%20%5Cfrac%7BX_%7BL%7D%20-%20X_%7BC%7D%7D%7BR%7D%29)
![\phi =tan^{-1}( \frac{47.12 - 0.636}{2399.5}) = tan^{-1}{0.0.01937}](https://tex.z-dn.net/?f=%5Cphi%20%3Dtan%5E%7B-1%7D%28%20%5Cfrac%7B47.12%20-%200.636%7D%7B2399.5%7D%29%20%3D%20tan%5E%7B-1%7D%7B0.0.01937%7D)
![\phi = 1.11^{\circ}](https://tex.z-dn.net/?f=%5Cphi%20%3D%201.11%5E%7B%5Ccirc%7D)
Mechanical advantage is defined as the ratio of output load to the input load. The mechanical advantage of the machine will be 0.1.
<h3>What is
mechanical advantage?</h3>
Mechanical advantage is a measure of the ratio of output force to input force in a system,
It is used to obtain the efficiency of forces in levers and pulleys. It is an effective way of amplifying the force in simple machines like levers.
The theoretical mechanical advantage is defined as the ratio of the force responsible for the useful work in the system to the applied force.
Given
applied force = 250 N
Output force = 25
Mechanical advantage = work output / work input
![\rm{Mechanical advantage}=\frac{F_O}{F_I}](https://tex.z-dn.net/?f=%5Crm%7BMechanical%20advantage%7D%3D%5Cfrac%7BF_O%7D%7BF_I%7D)
![\rm{Mechanical advantage}=\frac{25}{250}](https://tex.z-dn.net/?f=%5Crm%7BMechanical%20advantage%7D%3D%5Cfrac%7B25%7D%7B250%7D)
![\rm{Mechanical advantage}=0.1](https://tex.z-dn.net/?f=%5Crm%7BMechanical%20advantage%7D%3D0.1)
Hence the mechanical advantage of the machine will be 0.1
To learn more about the mechanical advantage refer to the link;
brainly.com/question/7638820
The final momentum of the body is equal to 120 Kg.m/s.
<h3>What is momentum?</h3>
Momentum can be described as the multiplication of the mass and velocity of an object. Momentum is a vector quantity as it carries magnitude and direction.
If m is an object's mass and v is its velocity then the object's momentum p is:
. The S.I. unit of measurement of momentum is kg⋅m/s, which is equivalent to the N.s.
Given the initial momentum of the body = Pi = 20 Kg.m/s
The force acting on the body, Pf = 25 N
The time, Δt = 4-0 = 4s
The Force is equal to the change in momentum: F ×Δt = ΔP
25 × 4 = P - 20
100 = P - 20
P = 100 + 20 = 120 Kg.m/s
Therefore, the final momentum of a body is 120 Kg.m/s.
Learn more about momentum, here:
brainly.com/question/4956182
#SPJ1
Explanation:
Acceleration is change in velocity over change in time:
a = Δv / Δt
a = (10 m/s - 25 m/s) / (240 s - 0 s)
a = -0.0625 m/s²
So the car decelerates at 0.0625 m/s².
<span>Because of the orbit of the earth and the sun and the moon. </span>