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I’m wondering what it means when the emf of a battery is calculated to be a negative value through Kirchhoff’s Voltage Law. This is the problem: Kirchhoff

As you can see, we’re given the currents, and we can also see that the two batteries are in series. Therefore, the emf of the center battery should be positive as well. However, the calculations depicted lead to a negative value.

Why does this happen, and what does this mean? Normally, I’d assume it is because this battery’s voltage opposes that of the other battery, but that is evidently not the case here.

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  • $\begingroup$ It means that the battery is turning the opposite way of what is drawn $\endgroup$ – Steeven Oct 11 at 7:27
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As @Steeven points out, the battery polarity is actually the reverse of that shown.

Just like loop currents in loop analysis are generally initially unknown, the center battery emf here is an unknown. For loop currents a direction is initially assumed. If after solving the loop equations a loop current turns out to be negative, it simply meant the assumed direction of the current was the reverse of the actual direction.

The same concept applies here, but in this case the polarity of the center battery was assumed to be as drawn. After doing the loop equation you found the assumed polarity of the center battery to be the opposite of what it actually is.

Hope this helps.

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