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 distance between a trough and a crest is double the amplitude.
The distance between trough and crest is (9m - 6m) = 3m.
So the amplitude of those water waves is (3/2) = 1.5 meters.
For this question, we really don't need to know how far apart the crests are, or how often they pass. There may be more parts to the question, for which that information is needed.
For example:
-- What's the wavelength of the waves ? 8 meters.
-- What's the period of the waves ? 4 seconds.
-- What's the frequency of the waves ? 1 / (4 seconds) = 0.25 Hz.
-- What's the speed of the waves ? (8 m) x (0.25 Hz) = 2 m/s
Line the outside of the cup with the tinfoil. Then put the cotton balls inside. Finally, line the cotton balls with the tinfoil and smush it all together.
Hey there! <span>The cohesive forces between liquid molecules are responsible for the phenomenon known as </span>surface tension<span>. The molecules at the </span>surface do<span> not have other like molecules on all sides of them and consequently they cohere more strongly to those directly associated with them on the </span>surface<span>. Hope this helps! :)</span>
Independent variable
The independent variable is the variable that is controlled and manipulated by the experimenter. For example, in an experiment on the impact of sleep deprivation on test performance, sleep deprivation would be the independent variable.
