Question

A large lightning bolt had a 20,000-A current and moved 30.0 C of charge. What was its duration?

a) 0.0015 s
b) 0.0030 s
c) 0.015 s
d) 0.030 s

Answer 1

The duration of the lightning bolt was \(0.0015\) seconds (a), calculated using
`\(t = (Q)/(I)\) with \(Q = 30.0\) C and \(I = 20,000\)` A.

Step-by-step explanation:

The formula relating charge (Q), current (I), and time (t) is:

[Q = I times t]

Given that the lightning bolt had a current (I) of 20,000 A and moved 30.0 C of charge (Q), rearranging the formula gives:

`\[t = (Q)/(I)\]`

Substituting the values:

`\[t = \frac{30.0 \, \text{C}}{20,000 \, \text{A}} = 0.0015 \, \text{s}\]`

Therefore, the duration of the lightning bolt was 0.0015 seconds.

When calculating the duration of a lightning bolt, the relationship between charge, current, and time is crucial. In this case, the equation Q = I * t governs the relationship between charge (Q), current (I), and time (t). Given that the lightning bolt had a current of 20,000 amperes and moved a charge of 30.0 coulombs, rearranging the formula to solve for time (t) yields t = Q / I. Substituting the provided values, the calculation shows that the duration of the lightning bolt was 0.0015 seconds.

The formula demonstrates that the time duration is directly proportional to the charge and inversely proportional to the current. Thus, a higher current would result in a shorter duration for the same amount of charge moved. In this scenario, the lightning bolt's significant current of 20,000 A led to a brief duration of just 0.0015 seconds to move the given charge of 30.0 C, emphasizing the intense power and rapid discharge associated with lightning events.so the correct option is a.

Answer 2

The duration of the lightning bolt with a 20,000-A current and moving 30.0 C of charge is 0.015 s. Thus option C is correct.

Step-by-step explanation:

To determine the duration of the lightning bolt, we can use the equation:

Charge = Current ×Time

Given that the current (I ) is 20,000 A and the charge (Q) is 30.0 C, we rearrange the formula to solve for time (t):

t=
`(Q)/(I)`

Substituting the values:

t =
`(30.0 C)/(20,000 A)`

t = 0.0015 s

However, this value is in seconds, not the units specified in the options. To convert seconds to the required format (milliseconds), we use the conversion factor:

0.0015 s = 0.0015 × 1000ms = 1.5 ms

The closest option to 1.5 milliseconds is c) 0.015 s, which translates to 15 milliseconds. Hence, the correct answer is c) 0.015 s.

This lightning bolt lasted for 0.015 seconds, which may seem extremely short, but it's typical for lightning, which occurs in a fraction of a second. The enormous current of 20,000 amperes passing through 30.0 coulombs of charge in this brief period demonstrates the intense energy released during a lightning strike. This calculation underscores the rapid and powerful nature of electrical discharges like lightning, emphasizing the tremendous energy released in a remarkably short time span. The safety precautions around lightning storms are crucial due to their sudden and potent nature, as this brief duration can cause substantial damage. Thus option C is correct.