Answer:
V = -RC (dV/dt)
Solving the differential equation,
V(t) = V₀ e⁻ᵏᵗ
where k = RC
Explanation:
V(t) = I(t) × R
The Current through the capacitor is given as the time rate of change of charge on the capacitor.
I(t) = -dQ/dt
But, the charge on a capacitor is given as
Q = CV
(dQ/dt) = (d/dt) (CV)
Since C is constant,
(dQ/dt) = (CdV/dt)
V(t) = I(t) × R
V(t) = -(CdV/dt) × R
V = -RC (dV/dt)
(dV/dt) = -(RC/V)
(dV/V) = -RC dt
∫ (dV/V) = ∫ -RC dt
Let k = RC
∫ (dV/V) = ∫ -k dt
Integrating the the left hand side from V₀ (the initial voltage of the capacitor) to V (the voltage of the resistor at any time) and the right hand side from 0 to t.
In V - In V₀ = -kt
In(V/V₀) = - kt
(V/V₀) = e⁻ᵏᵗ
V = V₀ e⁻ᵏᵗ
V(t) = V₀ e⁻ᵏᵗ
Hope this Helps!!!
The potential energy of the spring is 6.75 J
The elastic potential energy stored in the spring is given by the equation:
where;
k is the spring constant
x is the compression/stretching of the string
In this problem, we have the spring as follows:
k = 150 N/m is the spring constant
x = 0.3 m is the compression
Substituting in the equation, we get
Therefore. the elastic potential energy stored in the spring is 6.75J .
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Answer:
15 because 5×5×5 is the same thing as 5×3 which equals to 15
A transformer is designed to change 109 VV into 13,500 VV, and there are 120 turns in the primary coil. The secondary coil will have 14862 turns
A step-up transformer is a transformer that increases the voltage from the primary coil to the secondary coil while managing the same power at the rated frequency in both coils. It converts low voltage & high current from the primary side to the high voltage & low current on the secondary side of the transformer.
Ns = number of turns on the secondary coil = ?
Np = number of turns on the primary coil = 120
Vs = voltage across the secondary coil = 13500
Vp = voltage across the primary coil = 109
= 
109/13500 = 120 / Ns
Ns = 14862 turns
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The kinematic relations allow finding that the answers for the velocity and the position of the car in a time of 2 s. are:
- The velocity is v = 7 m / s
Kinematics studies the movement of bodies giving relationships between the position, velocity and acceleration of the body
They indicate that the initial velocity is v₀ = 1 m/s, that the car has an acceleration of a = 3 m/s² and asks about the position and velocity after a time of t = 2s
Let's used the kinematics relation
v = v₀ + a t
v = 1 + 3 2
v = 7 m / s
We look for the position
x = v₀ t + ½ a t²
x = 1 2 + ½ 3 2²
x = 8m
In conclusion, using the kinematics relations we can find the answers for the speed and the position of the car in a time of 2 S. They are
- The velocity is v = 7 m / s
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