Quick question of electricity flow

In summary, measurements with microelectrodes have shown that a 0.30-nm-diameter potassium ion (K+) channel carries a current of 1.8 pA. If the ion channel opens for 1.0 ms, approximately 11.25 billion potassium ions will pass through. The current density in the ion channel is 0.0024 pA/nm^2. To solve for the number of ions passing through, the equation I = n*A*q*Velocity can be used, where n is the number of ions, A is the area of the ion channel, q is the charge of each ion, and Velocity is the velocity of the ions. Using the definition of an ampere, it can be
  • #1
kyang002
22
0
Measurements with microelectrodes have shown that a 0.30-nm-diameter potassium ion (K+) channel carries a current of 1.8 pA.

How many potassium ions pass through if the ion channel opens for 1.0 ms?

What is the current density in the ion channel?

I am completely lost for this one. Anyone know of any equations that I can use?

Current is, its I = dQ/dt, the flow of charge through a point, through time. Like measuring the flow of water through a pipe.
The area the flow is going through (the inner area of the "pipe") because they give you the diameter. area = pi*r^2, 2*r = diameter.

I = dQ/dt = n*A*q*dx/dt = n*A*q*Velocity
so first solve I = n*A*q*Velocity

then use that with velocity = dx/dt to get dx.
Then use dQ = (n*A*dx)*q
to get dQ.

But I am stuck on how to solve for the variables and how to complete the problem. Can anyone help me out with the answer?
 
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  • #2
Needless to say, you're making this more difficult than you need to. What's the definition of an ampere? One ampere is one coulomb of charge moving past a fixed point each second. Each potassium ion has a fixed charge, +e. One coloumb of charge contains 6.25 * 10^18 such ions.

[tex]1.8 pA = \frac{1.8 \cdot 10^{-12} C}{s} \cdot \frac{6.25 \cdot 10^{18} \textrm{ ions}}{C} \cdot 1 \cdot 10^{-3} s[/tex]

Perform the multiplication and get your answer in number of ions.

- Warren
 
  • #3


To solve for the number of potassium ions passing through in 1.0 ms, we can use the equation dQ = n*A*q*dx, where dQ is the charge passing through, n is the number of ions, A is the area of the ion channel, q is the charge of each ion, and dx is the distance the ions travel in 1.0 ms. We can rearrange this equation to solve for n: n = dQ/(A*q*dx).

Plugging in the given values, we get n = (1.8 pC)/(π*(0.30/2)^2*1.6*10^-19 C*0.30 nm*10^-9 m/nm) = 3.0*10^5 ions.

To calculate the current density in the ion channel, we can use the formula J = I/A, where J is the current density, I is the current, and A is the cross-sectional area of the channel. Plugging in the given values, we get J = (1.8 pA)/(π*(0.30/2)^2) = 1.2*10^-6 A/m^2.
 

1. How does electricity flow through a circuit?

Electricity flows through a circuit due to the movement of electrons. When a voltage source, such as a battery, is connected to a closed circuit, it creates a potential difference that causes electrons to flow from the negative terminal to the positive terminal, completing the circuit.

2. What factors affect the flow of electricity?

The flow of electricity can be affected by various factors such as the type and size of the conductor, the resistance of the circuit components, the voltage and current in the circuit, and the presence of external factors like temperature and magnetic fields.

3. How does resistance impact the flow of electricity?

Resistance is the measure of how difficult it is for electricity to flow through a material. The higher the resistance, the more difficult it is for electricity to flow. As resistance increases, the flow of electricity decreases, and vice versa.

4. What is the difference between AC and DC current?

AC (alternating current) and DC (direct current) are two types of electric current. AC current changes direction periodically, while DC current flows in one direction. Most household appliances use AC current, while batteries and electronic devices typically use DC current.

5. What is the role of voltage in the flow of electricity?

Voltage is the driving force behind the flow of electricity. It is the measure of the potential difference between two points in a circuit. The higher the voltage, the greater the force pushing the electrons to flow and the stronger the current will be.

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