What is the Energy Calculation for a Bolt of Lightning?

[SAT2400]

Energy? Please help! (ToT)

Homework Statement

A bolt of lightning corresponding to about 20C descends through a potential difference of upwards of 150MV. How much energy is involved? Incidently, at anyone time there might be 2000 thunderstorms rolling over the Earth with 100 lightning bolts flashing every second!

Homework Equations

change in V= PE/q

The Attempt at a Solution

I know MV is 1000000V...but I have no idea how to solve this question...T_T please help ASAP..
Thank you very much!

 

[fatra2]

It has been a long time that I did problems like that. So I'll give it a shot, which might not be the same as what you have learned in school:

The energy involved is the power of the lightning bolt per time unit.
The power of an electrical current is the current times the voltage.
The electrical current is the amount of charge displace per time unit.
Put all of that into an equation and you should have a pretty simple answer.

Cheers

 

[SAT2400]

umm...okay...but I still don't know what to do?? T_T

Can you please explain more in detail?!T_T

I don't know the electrical current...etc...T_T

Please help! Thank you soo much!

 

[fatra2]

The energy involved is the power of the lightning bolt per time unit: [tex]P = \frac{\Delta E}{\Delta t}[/tex]
The power of an electrical current is the current times the voltage: [tex]P = V \cdot I[/tex]
The electrical current is the amount of charge displace per time unit: [tex]I = \frac{\Delta Q}{\Delta t}[/tex]

Can't really go any further, without giving the numerical answer. Cheers

 

[SAT2400]

The answer is 3000000000J(= 3x10^9)

I seriously don't know how to get this answer??! T_T how do I get current and time..?!?

Please help me again! Thank you very mucH!

 

[fatra2]

The answer seems correct.

You have only two data in your problem. Try multiplying them together, and it will give you that number.

Cheers

 

[SAT2400]

oh...so just 150MV x 20C??

but,,I don't get why I multiply V by C??!

Could you explain!? Thanks!:)

 

[fatra2]

I'll try my best.

The power is defined as the energy involved per time unit: [tex]P = \frac{\Delta E}{\Delta t}[/tex]

The power of an electrical discharge is given by: [tex]P = V \cdot I[/tex]

It is the same power in the two equations, therefore: [tex]\frac{\Delta E}{\Delta t} = P = V \cdot I[/tex]

But since the electrical current is defined as the discharge per time unit: [tex]I = \frac{\Delta Q}{\Delta t}[/tex]

[tex]\frac{\Delta E}{\Delta t} = V \cdot \frac{\Delta Q}{\Delta t}[/tex]
[tex]\Delta E = V \cdot \Delta Q[/tex]

Cheers

 

[SAT2400]

THANK YOU!

BTW...CHANGE IN Q is DISCHARGE??not CHARGE??

What do you mean by discharge??

hmm...
Equations like these (Q= Qmax e^(-t/RC), I =Imax e^(-t/RC)...etc.. show the DISCHARGE.. Right?
Can you explain these formulas?? Discharge means what??

 

[fatra2]

A discharge is defined by moving charges, e.g. lightning discharge is an amount of charge that is transported between the ground and the clouds.

Cheers

 

[SAT2400]

Discharge is moving charge?!?

Then,,what about the charge??

What's the difference btwn Discharge and Charge?!?

Q= Qmax e^(-t/RC), I =Imax e^(-t/RC)... For Discharge

Q=Qmax(1-e^-t/RC), I =Imax (1-e^(-t/RC)...For Charge

Could you please tell me the difference?!?Thank you!

 

[fatra2]

No. A discharge is not moving charge. It is just a term used to say that charges are conveyed in a lightning. The dictionary also states that discharges is the release of electrical energy. Precisely what we are talking about here.

For the rest of your question, I don't remember the precise meaning of the equations you are presenting. From what I can see, they could be applied in an RC circuit.

Here I am talking about definition only.
1. power is defined as the amount of energy per time unit
2. the current is defined as the amount of charge moved per time unit.
3. the power of an electrical current is given by the product of the voltage and current.

Hope this clarifies a bit of your problem. Otherwise, I can only suggest that you drop by to your teachers office, and asked for more information. I am sure that he/she will be glad to help you out with this issue.

Cheers

 

[diazona]

Q= Qmax e^(-t/RC), I =Imax e^(-t/RC)... For Discharge

Q=Qmax(1-e^-t/RC), I =Imax (1-e^(-t/RC)...For Charge

Those do indeed apply only to an RC circuit. In that context - and that context only - "discharging" refers to a situation in which the capacitor is losing charge, and "charging" refers to a situation in which the capacitor is gaining charge.

Those equations have nothing at all to do with lightning.

 

[SAT2400]

Thank you very much!

Could you please answer my other questions!?(in other threads!?)

I'm waiting for answers b/c I have a test tomorrow T_T;;