<span>1) The differential equation that models the RC circuit is :
(d/dt)V_capacitor </span>+ (V_capacitor/RC) = (V_source/<span>RC)</span>
<span>Where the time constant of the circuit is defined by the product of R*C
Time constant = T = R*C = (</span>30.5 ohms) * (89.9-mf) = 2.742 s
2) C<span>harge of the capacitor 1.57 time constants
1.57*(2.742) = 4.3048 s
The solution of the differential equation is
</span>V_capac (t) = (V_capac(0) - V_capac(∞<span>))e ^(-t /T) + </span>V_capac(∞)
Since the capacitor is initially uncharged V_capac(0) = 0
And the maximun Voltage the capacitor will have in this configuration is the voltage of the battery V_capac(∞) = 9V
This means,
V_capac (t) = (-9V)e ^(-t /T) + 9V
The charge in a capacitor is defined as Q = C*V
Where C is the capacitance and V is the Voltage across
V_capac (4.3048 s) = (-9V)e ^(-4.3048 s /T) + 9V
V_capac (4.3048 s) = (-9V)e ^(-4.3048 s /2.742 s) + 9V
V_capac (4.3048 s) = (-9V)e ^(-4.3048 s /2.742 s) + 9V = -1.87V +9V
V_capac (4.3048 s) = 7.1275 V
Q (4.3048 s) = 89.9mF*(7.1275V) = 0.6407 C
3) The charge after a very long time refers to the maximum charge the capacitor will hold in this circuit. This occurs when the voltage accross its terminals is equal to the voltage of the battery = 9V
Q (∞) = 89.9mF*(9V) = 0.8091 C
Answer:
The answer to the question is
The ball will go 0.14 meters high if the gun is aimed vertically
Explanation:
The energy in the spring → Energy, E =
Where E = energy in the spring
k = Spring constant
x = Spring compression or stretch
Therefore E =
The spring energy is transferred to the ball as kinetic energy based on the first law of thermodynamics which states that energy is neither created nor destroyed
Kinetic energy = KE =
From which v = = = 1.66 m/s
from v² =u² - 2·a·S
Where v = final velocity = 0 m/s
u = initial velocity = 1.66 m/s
a = g = Acceleration due to gravity
S = height
Therefore 0 = 1.66² - 2×9.81×S
or S = 1.66² ÷ (2×9.81) = 0.14 m
The aggregate of all the given moment of inertia's will be the moment of inertia of this system.
as, moment of inertia is given as
l = m * r^2
so, finding the moment of inertia of all the individual and adding them
<span>I=2∗<span>1^2</span>+1∗<span>2^2</span>+.5∗<span>2.5^2
</span>=9.125</span>
Answer:
6hrs
Explanation:
t = time taken until the trains pass by each other/hrs
38 + 54 = 92
Use time = distance/speed:
t = 552/92 = 6
Answer:
Conceptos y Magnitudes en
Fsica
Luciano LarozeNicols Porras Gonzalo Fuster
Ltda.
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