During a lightning storm, a lighting bolt causes 100 C of charge to move through a potential difference of 5 x 105 V. If the power associated with the lightening strike is 4 x 108 W, how long did the strike last? 0.350 s 0.125 s 100 s 0.023 S None of the above

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Chapter25: Electric Potential
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### Question 9 of 22

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**Problem Statement:**

During a lightning storm, a lightning bolt causes 100 C of charge to move through a potential difference of \(5 \times 10^5\) V. If the power associated with the lightning strike is \(4 \times 10^8\) W, how long did the strike last?

**Options:**

- ( ) 0.350 s
- ( ) 0.125 s
- ( ) 100 s
- ( ) 0.023 s
- ( ) None of the above

### Explanation:

To determine how long the lightning strike lasted, we need to use the equation relating power (P), voltage (V), charge (Q), and time (t). The equation is derived from the relationship:

\[ P = \frac{V \times Q}{t} \]

Rearranging the formula to solve for time (t), we get:

\[ t = \frac{V \times Q}{P} \]

Substitute the given values into the equation:

\[ V = 5 \times 10^5 \, \text{V} \]
\[ Q = 100 \, \text{C} \]
\[ P = 4 \times 10^8 \, \text{W} \]

So,

\[ t = \frac{5 \times 10^5 \, \text{V} \times 100 \, \text{C}}{4 \times 10^8 \, \text{W}} \]
\[ t = \frac{5 \times 10^7}{4 \times 10^8} \]
\[ t = 0.125 \, \text{s} \]

Therefore, the correct answer is:

- (•) 0.125 s
Transcribed Image Text:### Question 9 of 22 --- **Problem Statement:** During a lightning storm, a lightning bolt causes 100 C of charge to move through a potential difference of \(5 \times 10^5\) V. If the power associated with the lightning strike is \(4 \times 10^8\) W, how long did the strike last? **Options:** - ( ) 0.350 s - ( ) 0.125 s - ( ) 100 s - ( ) 0.023 s - ( ) None of the above ### Explanation: To determine how long the lightning strike lasted, we need to use the equation relating power (P), voltage (V), charge (Q), and time (t). The equation is derived from the relationship: \[ P = \frac{V \times Q}{t} \] Rearranging the formula to solve for time (t), we get: \[ t = \frac{V \times Q}{P} \] Substitute the given values into the equation: \[ V = 5 \times 10^5 \, \text{V} \] \[ Q = 100 \, \text{C} \] \[ P = 4 \times 10^8 \, \text{W} \] So, \[ t = \frac{5 \times 10^5 \, \text{V} \times 100 \, \text{C}}{4 \times 10^8 \, \text{W}} \] \[ t = \frac{5 \times 10^7}{4 \times 10^8} \] \[ t = 0.125 \, \text{s} \] Therefore, the correct answer is: - (•) 0.125 s
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