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Naddika [18.5K]
3 years ago
10

The membrane that surrounds a certain type of living cell has a surface area of 4.7 x 10-9 m2 and a thickness of 1.3 x 10-8 m. A

ssume that the membrane behaves like a parallel plate capacitor and has a dielectric constant of 4.7. (a) The potential on the outer surface of the membrane is 79.5 mV greater than that on the inside surface. How much charge resides on the outer surface
Physics
1 answer:
vagabundo [1.1K]3 years ago
6 0

Answer:

Q = 1.2*10⁻¹² C

Explanation:

  • For any capacitor, by definition the capacitance C is equal to the relationship between the charge on one of the conductors and the potential difference between them, as follows:

       C = \frac{Q}{V}  (1)

  • For the special case of a parallel plate capacitor, just by application of Gauss' law to a rectangular surface half out of the outer surface, and half inside it, it can be showed that the value of the capacitance C is a parameter defined only by geometric constants, as follows:

       C = \frac{\epsilon_{0}*\epsilon _{r} * A}{d}  (2)

  • So, due to the left sides in (1) and (2) are equal each other, right sides must be equal too.
  • Replacing ε₀, εr (dielectric constant), A, d and V by their values, we can solve for Q, as follows:

       Q =\frac{\epsilon_{0} * \epsilon_{r} *A* V}{d} = \frac{(8.85*(4.7)^{2}*79.5)e-24 (F/m*m2*V)}{1.3e-8m} =  1.2e-12 C = 1.2 pC  (3)

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A tall tube is evacuated and its stopcock is closed. The open end of the tube is immersed in a container of water (density 10^3
LuckyWell [14K]

Answer:

10.19 m

Explanation:

Water will rise to equalize the pressure inside and outside the tube.

The equation of pressure is given by

p=\rho gh

Where,

p = Pressure of air = 10⁵ N/m²

ρ = Density of water = 10³ kg/m³

g = Acceleration due to gravity = 9.81 m/s²

h = Height the water will rise

h=\frac{p}{gh}\\\Rightarrow h=\frac{10^5}{9.81\times 10^3}\\\Rightarrow h=10.19\ m

∴ The water will rise by 10.19 m.

7 0
3 years ago
A coil with an inductance of 2.3 H and a resistance of 14 Ω is suddenly connected to an ideal battery with ε = 100 V. At 0.13 s
klemol [59]

Given Information:

Resistance = R = 14 Ω

Inductance = L = 2.3 H

voltage = V = 100 V

time = t = 0.13 s

Required Information:

(a) energy is being stored in the magnetic field

(b) thermal energy is appearing in the resistance

(c) energy is being delivered by the battery?

Answer:

(a) energy is being stored in the magnetic field ≈ 219 watts

(b) thermal energy is appearing in the resistance ≈ 267 watts

(c) energy is being delivered by the battery ≈ 481 watts

Explanation:

The energy stored in the inductor is given by

U = \frac{1}{2} Li^{2}

The rate at which the energy is being stored in the inductor is given by

\frac{dU}{dt} = Li\frac{di}{dt} \: \: \: \: eq. 1

The current through the RL circuit is given by

i = \frac{V}{R} (1-e^{-\frac{t}{ \tau} })

Where τ is the the time constant and is given by

\tau = \frac{L}{R}\\ \tau = \frac{2.3}{14}\\ \tau = 0.16

i = \frac{110}{14} (1-e^{-\frac{t}{ 0.16} })\\i = 7.86(1-e^{-6.25t})\\\frac{di}{dt} = 49.125e^{-6.25t}

Therefore, eq. 1 becomes

\frac{dU}{dt} = (2.3)(7.86(1-e^{-6.25t}))(49.125e^{-6.25t})

At t = 0.13 seconds

\frac{dU}{dt} = (2.3) (4.37) (21.8)\\\frac{dU}{dt} = 219.11 \: watts

(b) thermal energy is appearing in the resistance

The thermal energy is given by

P = i^{2}R\\P = (7.86(1-e^{-6.25t}))^{2} \cdot 14\\P = (4.37)^{2}\cdot 14\\P = 267.35 \: watts

(c) energy is being delivered by the battery?

The energy delivered by battery is

P = Vi\\P = 110\cdot 4.37\\P = 481 \: watts

4 0
3 years ago
5. Find the mass of a car that is traveling at a velocity of 35 m/s West.
sattari [20]

Answer:

m = 9795.9 kg

Explanation:

v = 35 m/s

KE = 6,000,000 J

Plug those values into the following equation:

KE = \frac{1}{2} mv^{2}

6,000,000 J = (1/2)(35^2)m

---> m = 9795.9 kg

3 0
3 years ago
In major league baseball, the pitcher's mound is 60 feet from the batter. If a pitcher throws a 85 mph fastball, how much time e
Nostrana [21]
The given from your problem are the following:
V = 85mph (This is miles per hour)
d = 60 feet

If you notice the units do not match. Before we can do anything else, we need to make the figures match. 

In this case, we will convert 85miles per hour to feet per hour.  There are 5,280 feet in 1 mile. 
\frac{85miles }{hr} x \frac{5,280feet}{1miles} = \frac{448,800feet}{hr}

But wait! If you think about the scenario, you are looking for how long it will take for the ball to reach the bat. The most applicable unit of time to use here is second. It would be very hard to really measure a short and instantaneous event in hours. So we convert it into feet per second: 

There are 3,600 seconds in 1 hour.

\frac{448,800feet }{hour} x \frac{1hour}{3,600seconds} = \frac{448,800feet}{3,600 seconds} = 124.67ft/s

So now we have our new given as:

v = 124.67ft/s
d = 60 ft

The formula for time can be derived from the formula from velocity, which is:
velocity = \frac{distance}{time}

The formula of time will then be:
time= \frac{distance}{velocity}

All you need to do is plug in what you know and solve for what you don't know. 

time= \frac{60feet}{124.67ft/s}

time= 0.48s

The answer then is 0.48s.

If you want this in hours, just divide the value in seconds by 3,600. The answer would then be 0.00013hr. (See how small it is? This is why seconds would be a more appropriate measure.)
8 0
3 years ago
Wire sizes are often reported using the AWG (American Wire Gauge) system in which smaller diameter wires are said to be of highe
NISA [10]

Answer:

Explanation:

24 - gauge wire , diameter = .51 mm .

Resistivity of copper ρ = 1.72 x 10⁻⁸ ohm-m

R = ρ l / s

1.72x 10⁻⁸ / [3.14 x( .51/2)² x 10⁻⁶ ]

= 8.42 x 10⁻² ohm

= .084 ohm

B )  Current required through this wire

= 12 / .084 A

= 142.85 A

C )

Let required length be l

resistance = .084 l

2 = 12 / .084 l

l = 12 / (2 x .084)

= 71.42 m

6 0
3 years ago
Read 2 more answers
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