Current dependent on Voltage

In summary, the question asks for the maximum energy that a solar cell can deliver to a load per year, given its current-voltage characteristic and assuming 12 hours of sunlight per day. Using the equation P=IV, the optimal angle for maximum power can be found and used to calculate the total cumulative energy over a year.
  • #1
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Homework Statement



A solar cell has a current–voltage characteristic given by [tex]I=I_0\cos\(\frac{\pi V}{2V_0}\)[/tex] where [tex]I_0[/tex] and [tex]V_0[/tex] are given constants. If the sun shines 12 out of 24 hours what is the maximum energy that can the cell can deliver to a load per year?

Homework Equations



[tex]P=IV[/tex]

The Attempt at a Solution



Somehow I get the feeling this is incredibly simple and I'm just missing something. But anyhow, using [tex]P=IV[/tex] I get [tex]P=I_0\cos\(\frac{\pi V}{2V_0}\)V[/tex]. Then taking [tex]\frac{dP}{dV}[/tex] to find a maximum, I get [tex]\tan z = z^{-1}[/tex] where [tex]z=\frac{\pi V}{2V_0}[/tex]. Am I on the right track? Or am I missing something. Thanks!
 
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  • #2
Your approach looks correct... however the question seems strange. The power can be made arbitrarily high by making the voltage arbitrarily high and keeping the cosine term in phase... so I am confused...
 
  • #3
nicksauce said:
Your approach looks correct... however the question seems strange. The power can be made arbitrarily high by making the voltage arbitrarily high and keeping the cosine term in phase... so I am confused...

I agree the problem is confusing, but as V increases, I decreases, according to the given equation.

cos(0) = 1, cos(PI/4) = 1/SQRT(2), cos(PI/2) = 0

So you would want to find the angle where you get the greates product P = VI, and use that to calculate what the total cumulative energy is over a year (looks like they are assuming sun-tracking mounts for the solar cells).
 
  • #4
We are to assume that the angle of the cell w.r.t. the sun is maintained so that the given i-v characteristic is always true during daylight. The load on the cell can be adjusted in order to get the current and voltage that results in maximum power.
 

1. What is the relationship between current and voltage?

The relationship between current and voltage is described by Ohm's law, which states that the current flowing through a conductor is directly proportional to the voltage applied across it. This means that as the voltage increases, the current also increases, and vice versa.

2. How does current depend on voltage in a circuit?

In a circuit, the current flow is determined by the voltage of the power supply and the resistance of the components in the circuit. The higher the voltage, the more energy is available to push the electrons through the circuit, resulting in a larger current.

3. What happens to current if voltage is held constant?

If the voltage in a circuit is held constant, the current will remain the same as long as the resistance also remains constant. This is because the relationship between current and voltage is linear and proportional, as described by Ohm's law.

4. How does resistance affect the relationship between current and voltage?

Resistance plays a crucial role in the relationship between current and voltage. The higher the resistance, the more difficult it is for current to flow, which means that a higher voltage is needed to maintain the same level of current. On the other hand, a lower resistance allows for a larger current flow at the same voltage.

5. Can current exist without voltage?

No, current cannot exist without voltage. Voltage is the driving force that pushes electrons through a circuit, so without voltage, there would be no movement of electrons and therefore no current flow.

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