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I'm currently studying the textbook Fundamentals of Electric Circuits, 7th edition, by Charles Alexander and Matthew Sadiku. Chapter 1.5 Power and Energy gives the following example:

Example 1.4

An energy source forces a constant current of 2 A for 10 s to flow through a light bulb. If 2.3 kJ is given off in the form of light and heat energy, calculate the voltage drop across the bulb.

Solution:

The total charge is $$\Delta q = i \Delta t = 2 \times 10 = 20 \text{ C}$$ The voltage drop is $$\nu = \dfrac{\Delta w}{\Delta q} = \dfrac{2.3 \times 10^3}{20} = 115 \text{ V}$$

Why does this solution say that "the total charge is" \$\Delta q\$, when \$\Delta q\$ actually is the difference/change in charge? I'm not sure whether I'm missing something here, or whether it's just an unusual choice of words.

The Pointer
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  • the word 'total' seems superfluous here, suggesting a disctinction where none exists. It's a loose and lazy use of language, beacuse, as you've demonstrated, it's obvious what the author actually means in the context. – Neil_UK Nov 04 '21 at 07:41
  • @Neil_UK Ok, thanks for the clarification. I guess we just trust in the mathematics, since that, unlike natural language, is unambiguous. – The Pointer Nov 04 '21 at 07:42
  • It could have an initial charge, and after 10s it is not fully discharged, so there is also the remaining charge, thus difference of charge. – Marko Buršič Nov 04 '21 at 08:04
  • Between what position/time is the difference taken ? I think the word "total" is appropriate since that is the total charge that passed through the light bulb during the conduct of the experiment. The word "difference" would be okay to use if we were talking about the charge imbalance between two plates of a capacitor or comparing the charge on an object at two different time instants. – AJN Nov 04 '21 at 08:07
  • Ok, thank you all for the input. – The Pointer Nov 04 '21 at 08:11

1 Answers1

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It's steady state problem. No transient calculations are requested.

Δq is the total charge that flows in the bulb in Δt time interval.

Enrico Migliore
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