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.

PHYSICS 1201 SU2025 (10585) Final Exam- Requires Respondus LockDown Browser

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)

查看解析

登录即可查看完整答案

类似问题

The basic unit for electric current is:

What are SI units of n and q in the formula I = nqvdA?

If there are +3 C of charges moving in the +x direction and -5 C of charges moving in the -x direction, what is the direction of the electric current and why?

What is an electric current and its SI unit?

'Electric Current' or 'Current': (select all that apply)

When charged particles move through a conductor such as copper wire, what moves? Select an answer from the options below. eTextbook and Media Links to an external site.

A current of 5.0 A flows through an electrical device for 10 seconds. How many electrons flow through this device during this time? (e = 1.60 × 10-19 C)

Conventional current refers to the direction that positive charges would move through a circuit. We use this convention when describing electricity in a circuit because...

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单