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Cerrena [4.2K]
3 years ago
13

Now solve the differential equation V(t)=−CRdV(t)dt for the initial conditions given in the problem introduction to find the vol

tage as a function of time for any time t. Express your answer in terms of q0, C, R, and t.
Physics
1 answer:
mina [271]3 years ago
8 0

Answer:

V(t) = (q0/C) * e^(−t/RC )

Explanation:

If there were a battery in the circuit with EMF  E , the equation for  V(t)  would be  V(t)=E−(RC)(dV(t)/dt) . This differential equation is no longer homogeneous in  V(t)  (homogeneous means that if you multiply any solution by a constant it is still a solution). However, it can be solved simply by the substitution  Vb(t)=V(t)−E . The effect of this substitution is to eliminate the  E  term and yield an equation for  Vb(t)  that is identical to the equation you solved for  V(t) . If a battery is added, the initial condition is usually that the capacitor has zero charge at time  t=0 . The solution under these conditions will look like  V(t)=E(1−e−t/(RC)) . This solution implies that the voltage across the capacitor is zero at time  t=0  (since the capacitor was uncharged then) and rises asymptotically to  E  (with the result that current essentially stops flowing through the circuit).

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3 years ago
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Based on the thermodynamic properties provided for water, determine the energy change when the temperature of 0.650 kg of water
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The boiling point of water is 100°C. So at 101°C, the water is steam. Compute the specific heat first from 101 to 100.

E = mCΔT, where c for steam is 1.996 kJ/kg·°C
E₁ = (0.65 kg)(1.996 kJ/kg·°C)(101 - 100°C) = 1.2974 kJ

Next, let's solve the latent heat when steam turns to liquid. The heat of vaporization of water is 2260 kJ/kg.

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Lastly, let's solve the energy to bring down the temperature to 51°C. The specific heat of liquid water is 4.187 kJ/kg·°C.
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4 0
3 years ago
Based on Archimedes' principle, the greatest buoyant force an object can experience in water is determined by which quantity?
ValentinkaMS [17]

Answer:

B. The object's volume

Explanation:

When an object is immersed in a fluid, it experiences an upward force which is called buoyant force. The magnitude of the buoyant force is given by:

B=\rho_f V_{disp} g

where

\rho_f is the density of the fluid in which the object is immersed

V_{disp} is the volume of the fluid displaced by the object

g is the acceleration due to gravity

When the object is totally immersed in the fluid, V_{disp} corresponds to the volume of the object; when the object is only partially immersed, V_{disp} corresponds only to the volume of the part of the object immersed.

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3 years ago
An ocean liner leaves New York City and travels 18.0o north of east for 155 km. How far east and how far north has it gone? In o
Monica [59]
I’m sorry if i took up a lot of space, hope this is a valid approximate answer

6 0
2 years ago
A spherical Christmas tree ornament is 8.00 cm in diameter. What is the magnification of an object placed 12.0 cm away from the
LiRa [457]

The magnification of the ornament is 0.25

To calculate the magnification of the ornament, first, we need to find the image distance.

Formula:

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make u the subject of the equation

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From the question,

Given:

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Substitute these values into equation 2

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Finally, to get the magnification of the ornament, we use the formula below.

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Where

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Substitute these values above into equation 3

  • M = 3/12
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Hence, The magnification of the ornament is 0.25

8 0
2 years ago
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