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Agata [3.3K]
2 years ago
7

The current in some DC circuits decays according to the function I=I0e−t/τ, where I is the current at some point in time, I0 is

the initial current at time t=0, and τ is the time constant determined by the properties of the circuit. If you start such a circuit with an initial current of 1.2 Amps, and find that after 3.5 seconds have passed it has a current of 0.2 Amps, what is the value of the time constant τ for this particular circuit?
Physics
1 answer:
almond37 [142]2 years ago
3 0

Answer: 1.95

Explanation:

You should start off from the decay formula and solve for τ:

I = I_{0}e^{\frac{t}{\tau\\  } }

\frac{I}{I_{0}} = e^{\frac{-t}{\tau} }

Apply inverse logarithmic function:

ln(\frac{0.2 A}{1.2 A} ) = \frac{-t}{\tau}

The final form will be:

\tau=\frac{-3.5s}{ln(\frac{0.2A}{1.2A} )}

Inputing values for I, IO, and t:

\tau=\frac{-3.5S}{ln(\frac{0.2 A}{1.2 A} )} = 1.95

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Answer:

the only effect it has is to create more induced charge at the closest points, but the net face remains zero, so it has no effect on the flow.

Explanation:

We can answer this exercise using Gauss's law

      Ф = ∫ e . dA = q_{int} / ε₀

field flow is directly proportionate to the charge found inside it, therefore if we place a Gaussian surface outside the plastic spherical shell.  the flow must be zero since the charge of the sphere is equal  induced in the shell, for which the net charge is zero. we see with this analysis that this shell meets the requirement to block the elective field

From the same Gaussian law it follows that if the sphere is not in the center, the only effect it has is to create more induced charge at the closest points, but the net face remains zero, so it has no effect on the flow , so no matter where the sphere is, the total induced charge is always equal to the charge on the sphere.

5 0
2 years ago
A mercury thermometer has a glass bulb of interior volume 0.100 cm3 at 10°c. the glass capillary 10) tube above the bulb has an
Nadya [2.5K]
Initial volume of mercury is
V = 0.1 cm³

The temperature rise is 35 - 5 = 30 ⁰C = 30 ⁰K.

Because the coefficient of volume expansion is 1.8x10⁻⁴ 1/K, the change in volume of the mercury is 
ΔV = (1.8x10⁻⁴ 1/K)*(30 ⁰K)(0.1 cm³) = 5.4x10⁻⁴ cm³

The cross sectional area of the tube is
A = 0.012 mm² = (0.012x10⁻² cm²).
Therefore the rise of mercury in the tube is
h = ΔV/A
   = (5.4x10⁻⁴ cm³)/(0.012x10⁻² cm²)
   = 4.5 cm

Answer: 4.5 cm
7 0
2 years ago
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Eratosthenes determined the circumference of Earth by conducting an experiment. Put his steps in order as they correlate to the
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Solution: The correct order is: C, A, B

The statement of the problem:

How can we prove Earth is round and calculate its circumference?

Hypotheis:

If the sun casts shadows at different angles at the same time of day in different places, we can determine how much Earth curves.

If the Earth was flat, the angle measured at different places at the same time of the day would be same.

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In Syene, the sun's rays are vertical at noon. At the same time in Alexandria, the rays are 7.2 degrees from the vertical.

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2 years ago
A 3.00-kg model airplane has velocity components of 5.00 m/s due east and 8.00 m/s due north. What is the plane’s kinetic energy
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Answer:

Kinetic energy, E = 133.38 Joules

Explanation:

It is given that,

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Let v is the resultant of velocity. It is given by :

v=\sqrt{v_1^2+v_2^2}

v=\sqrt{5^2+8^2}=9.43\ m/s

Let E is the kinetic energy of the plane. It is given by :

E=\dfrac{1}{2}mv^2

E=\dfrac{1}{2}\times 3\ kg\times (9.43\ m/s)^2

E = 133.38 Joules

So, the kinetic energy of the plane is 133.38 Joules. Hence, this is the required solution.

5 0
2 years ago
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"For a first order instrument with a sensitivity of .4 mV/K and a time" constant of 25 ms, find the instrument’s response as a f
ELEN [110]

Answer:

Explanation:

Given that:

For a first order instrument with a sensitivity of .4 mV/K

constant c  = 25 ms = 25 × 10⁻³ s

The initial temperature T_1 = 273 K

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The initial volume = 0.4 mV/K × 273 K = 109.2 V

The final volume =  0.4 mV/K × 473 K =  189.2 V

the instrument’s response as a function of time for a sudden temperature increase can be computed as follows:

Let consider y to be the function of time i.e y(t).

So;

y(t) = 109.2  + (189.2 - 109.2)( 1 - \mathbf{e^{-t/c}})mV

y(t) = (109.2 +  80 ( 1 - \mathbf{e^{t/25\times 10^{-3}}})) mV

Plot the response y(t) as a function of time.

The plot of y(t) as a function of time can be seen in the diagram  attached below.

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The unit for y(t) is mV.

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170.28 mV = (109.2 +  80 ( 1 - \mathbf{e^{t/25\times 10^{-3}}})) mV

170.28 mV - 109.2 mV = 80 ( 1 - \mathbf{e^{t/25\times 10^{-3}}})) mV

61.08 mV =  80 ( 1 - \mathbf{e^{t/25\times 10^{-3}}})) mV

0.7635  mV = ( 1 - \mathbf{e^{t/25\times 10^{-3}}})) mV

t = 1.44 × 25  × 10⁻³ s

t = 0.036 s

t = 36 ms

The error fraction = \dfrac{189.2-170.28  }{189.2}

The error fraction = 0.1

The error fraction = 10%

8 0
2 years ago
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