A total of 2.0 × 1013 electrons pass a given point in a wire in 15 s. What is the current in the wire? (e = 1.60 × 10-19 C)

Question

A total of 2.0 × 1013 electrons pass a given point in a wire in 15 s.  What is the current in the wire? (e = 1.60 × 10-19 C)

BlackTom AI · Accepted Answer

To approach this, I will compute the total charge that passes the point and then divide by the time to get the current.
Step 1: Find the total charge Q carried by the electrons. Each electron has charge e = 1.60 × 10^-19 C, and there are N = 2.0 × 10^13 electrons. Multiply to get Q = N × e = (2.0 × 10^13) × (1.60 × 10^-19 C) = 3.2 × 10^-6 C.
Step 2: Use the definition of current I = Q / t. The time is t = 15 s, so I = (3.2 × 10^-6 C) / (15 s) = 2.133... × 10^-7 A ≈ 2.13 × 10^-7 A.
Step 3: Convert to microamperes for easier comparison with the options: 1 A = 10^6 μA, so I ≈ 2.13 × 10^-7 A = 0.213 μA ≈ 0.21 μA.
Now evaluate the provided answer choices:
Option 1: 3.2 μA. This would correspond to a current roughly 15,000 times larger than the calculated value, which would occur if time were about 0.0002 s or if Q were about 3.2 × 10^-5 C. Neither matches our numbers, so this is incorrect.
Option 2: 1.3 mA. This is 1.3 × 10^-3 A, which is orders of magnitude larger than the computed 2.13 × 10^-7 A. It would require a charge on the order of 0.0195 C passing in 15 s, not the 3.2 × 10^-6 C we have, so this is incorrect.
Option 3: 1.3 A. This is far too large by about six to seven orders of magnitude relative to the calculation. As with the previous option, the required Q or t would have to be unrealistically different, so this is incorrect.
Option 4: 0.21 μA. This matches the calculation after converting units, since 0.213 μA rounds to 0.21 μA. The steps above show Q and t leading to this current value, so this is the correct choice.
End result: the correct magnitude is obtained when dividing the total charge 3.2 × 10^-6 C by 15 s and converting to microamperes, yielding approximately 0.21 μA.

A total of 2.0 × 1013 electrons pass a given point in a wire in 15 s. What is the current in the wire? (e = 1.60 × 10-19 C)单项选择题

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