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Difficulty: MediumElectrical Current and Electron Flow

During a maintenance check on an emergency backup power system, an ammeter registers a continuous reading of 4 amperes4\text{ amperes} through a primary feeder wire. How many coulombs of electrical charge pass through any given cross-section of this feeder wire in 15 seconds15\text{ seconds}?

  1. A
    3.75 coulombs3.75\text{ coulombs}
  2. 60 coulombs60\text{ coulombs}Answer
  3. C
    0.27 coulombs0.27\text{ coulombs}
  4. D
    60 volts60\text{ volts}

Answer

60 coulombs60\text{ coulombs} of electrical charge pass through the cross-section.
Electric current in amperes measures the rate of charge movement where 1 ampere=1 coulomb per second1\text{ ampere} = 1\text{ coulomb per second}. Multiplying the steady current (4 A4\text{ A}) by the elapsed time (15 s15\text{ s}) gives the total charge transfer: 4 C/s×15 s=60 coulombs4\text{ C/s} \times 15\text{ s} = 60\text{ coulombs}.

Step-by-Step Solution

1
Identify the relationship between electric current, charge, and time
I=QtI = \frac{Q}{t}, where II is current in amperes, QQ is charge in coulombs, and tt is time in seconds
One ampere is defined as the flow of one coulomb of charge per second (1 A=1 C/s1\text{ A} = 1\text{ C/s}).
2
Rearrange the formula to solve for total charge QQ
Q=I×tQ = I \times t
Multiplying both sides of the rate equation by time isolates the total charge quantity.
3
Substitute the given values into the equation and compute the result
Q=4 A×15 s=60 CQ = 4\text{ A} \times 15\text{ s} = 60\text{ C}
Evaluating the product yields the total accumulated charge that traversed the wire.

Key Concept

Electric current is the time rate of electric charge transfer through a conductor (1 A=1 C/s1\text{ A} = 1\text{ C/s}).
Estimated Time:45s
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Topics

Electrical Current and Electron Flow

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