Solving an Electrical Problem: Why is the Answer Not 2s?

[john merrick]

Homework Statement

the charge passing through a circuit has 120J of energy. if the circuit is connected to a 12V battery and the current in the circuit is 0.5A how long does it take one coulomb of charge to pass through the circuit?

Relevant Equations

E=VIt
I=Q/t

i did this
t=Q/I 1C/0.5A =2s

the book says
E=VIt 120J=12v x 0.5A x t

t=20s.

i don't understand why the answer is not 2s.

 

[Delta2]

Well the problem statement seems a bit vague to me. If I interpret "the charge passing through a circuit has 120J of energy" as that the energy given from the battery to a certain amount of charge that travels one loop of the circuit is 120J, then your book is correct.
Your own calculation finds the time needed for 1 Coulomb of charge to pass through a cross section of the circuit, not through 1 loop of the circuit.

 

[Drakkith]

i did this
t=Q/I 1C/0.5A =2s

Notice that this equation doesn't include the given amount of energy, which is a clue that it's probably not what you're looking for. If I told you the energy was 240 J instead of 120, this equation would give you an identical answer for both.

Since the question involves both energy and time, that's a big clue that you're looking for something that includes power in it, which your book's equation does (the V*I portion).

Still, the question is poorly worded in my opinion. I can't remember ever discussing the time taken for an amount of charge to pass through a circuit in my basic electronics electric circuits class. A 0.5 amp current passes 10 coulombs of charge through each point in the circuit over 20 seconds (assuming a simple series circuit), so I don't understand what the question is talking about when asks about how long it takes for 1 coulomb to pass through the circuit.

What the book's answer really tells me is that it's looking for how long it takes to dissipate the 120 J of energy, not how long it takes for some quantity of charge to move through the circuit.