Energy stored in capacitance of a squid

In summary, the giant axon of a squid is 0.5 mm in diameter, 10 cm long, and unmyelinated, behaving as a capacitor with 1 microF capacitance per square centimeter of membrane area. The energy stored in this capacitance when charged to the -70 mV resting potential is 4*10^-9 J. The equation for energy stored in a capacitor is U = 1/2 CV^2. Using this equation, we can find the energy stored if we know the capacitance and voltage. In this case, the area of the axon is calculated using the surface area of a cylinder and the voltage is given as -70 mV. The final calculation results in
  • #1
rayhan619
77
0

Homework Statement



The giant axon of a squid is 0.5 mm in diameter, 10 cmlong, and not myelinated. Unmyelinated cell membranes behave as capacitors with 1 microF capacitance per square centimeter of membrane area.
When the axon is charged to the -70 mV resting potential, what is the energy stored in this capacitance?


Homework Equations



R = (density* length)/Area

The Attempt at a Solution



I know how to get R and C is given. and V is also given.
but how do i solve for E?
 
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  • #2
I have a few comments:

1. R is irrelevant here.

2. The capacitance is not 1 microF, in case that is what you are thinking. Read what it says carefully.

3. Your textbook should have a discussion of energy stored in a capacitor, along with an equation.
 
  • #3
Energy stored in a capacitor, U = 1/2(Q^2/C) = 1/2(Q/V) = 1/2 CV^2
If we know any two of Q,C, or V we can figure out the energy.
C is 1 microF per square centimeters. we can get the area using A=(3.14)r^2 and get the C from there.
and the V is given -70 mV.
so we can use V and C to get U.
right?
 
  • #4
Almost. Everything except for A is correct.

The area is a cylinder, not a circle. Use the surface area of a cylinder to get A, and you'll have it.
 
  • #5
so area for cylinder is, A = 2 pi r ( r + h ).
= 2(3.14)(2.5*10^-4){(2.5*10^-4)+0.1} m^2
= 1.57*10^-4 m^2
= 1.57 cm^2
so C = (1*10^-6 F)(1.57 cm^2)
= 1.57*10^-6 F
and V = -70 mV = -70*10^-3 V

Energy, E = 1/2 CV^2 = 1/2 (1.57*10^-6 F)(-70*10^-3 V)^2
= - 4 *10^-9 J

Does that look right?
 
  • #6
Looks good except that energy is positive. :smile:

(-70 mV)^2 = +4900 mV^2 > 0​
 
  • #7
oh ya. thanks
 

1. What is the energy stored in capacitance of a squid?

The energy stored in the capacitance of a squid refers to the amount of electrical energy that can be stored in the squid's electric organs. These organs contain specialized cells called electrocytes that can generate and store electricity.

2. How is the energy stored in capacitance of a squid measured?

The energy stored in capacitance of a squid can be measured by calculating the capacitance of the electric organs and the voltage at which they are able to discharge. This can be done using specialized equipment such as an oscilloscope.

3. What factors affect the energy stored in capacitance of a squid?

The energy stored in capacitance of a squid can be affected by various factors such as the size and number of electric organs, the type of electrocytes present, and the metabolic rate of the squid. These factors can impact the overall capacitance and voltage of the squid's electric system.

4. How does the energy stored in capacitance of a squid benefit the animal?

The energy stored in capacitance of a squid allows them to produce strong electric fields that are used for communication, navigation, and defense. It also enables them to stun or immobilize prey, making them efficient hunters.

5. Is the energy stored in capacitance of a squid renewable?

Yes, the energy stored in capacitance of a squid is renewable. The electric organs of the squid constantly produce and store new electricity, allowing them to use their electric abilities repeatedly. However, the amount of energy stored can decrease over time if the squid does not have access to a sufficient food source to maintain their metabolic rate.

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