1

What's the total charge that moves from one terminal of a battery to the other if 50mA of current are provided to a load for 1 hour?

I think I'm suppose to use the formula I = Q/t, where I is the current in amps, Q is Coulombs and t is time in seconds. The way I did the problem was to first multiply t to both sides so that I could isolate Q. Then rewrote the formula as Q = I x t. But I think that's wrong for some reason. I'm getting 50mA x 3600 = 180000C. Then convert it to 180 mC? so answer would be 180 mC? I don't think that's right so I'm asking here for some guidance.

echo
  • 31
  • You should get $180000$mC (milliamps means millicoloumbs) which yields $180$C. You did your conversion backwards, as far as I can tell. – Ian Coley Oct 04 '14 at 22:36
  • 1
    If it starts with milli the the answer is in milli, I think. I should of known that. Thanks and I guess I did the problem right then, besides the conversion error. Thank you. – echo Oct 04 '14 at 22:38
  • SI units: $I$ should be in $A$, $Q$ in $C$ and $t$ in $s$. – user5402 Oct 04 '14 at 22:44

1 Answers1

0

Battery capacities are typically measured in amp-hours. So 50ma for 1 hour is 50mAh.

If you want to measure in Coloumbs then use the conversion factor 1Amp-second = 1C, or one amp for 1 second represents 1 Coloumb of charge..

$$50 \mathrm{mAh} \cdot \frac{1 \mathrm{A}}{1000 \mathrm{mA}}\cdot \frac{1 C}{1 \mathrm{s} \cdot 1 \mathrm{A}} \cdot \frac{3600 \mathrm{s}}{1 \mathrm{h}} = 50 \cdot \frac{1}{1000} \cdot 1{C} \cdot 3600 = 180 \mathrm{C}$$

Each of the conversion factors is 1, and all the units cancel out except the Coloumb.

NovaDenizen
  • 4,216
  • 15
  • 23
  • Then would 50mAh be a legitimate answer for the total charge in this question? The reason I ask is this problem was given in the chapter right in the between the formula I = Q/t and Ah = I x t. I was kind of unsure which formula I should use on this problem. I guess I'm wondering if I should of use Ah = (I)(t) instead. – echo Oct 04 '14 at 23:17
  • If the question used the same wording you did ("What is the total charge that moves...") then the answer in Coloumbs is the correct one. People who use batteries in the real world tend to talk about capacities in amp-hours or volt-amp-hours. – NovaDenizen Oct 04 '14 at 23:19
  • Ok, yes it used the same wording. Thank you though, that is some great info.I am taking a DC Circuits class so all of this matters. – echo Oct 04 '14 at 23:20