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# Analyzing a resistor circuit with two batteries

An example of simplifying a seemingly complicated resistor circuit. Created by Willy McAllister.

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• What would happen if I had two batteries in parallel, and they had different voltages, say, 6V and 12V, what would be the voltage from the point they combine into one wire and another point on that wire ?
• Hello Feraru,

If you did this with real batteries I recommend you run away! There is a real risk of explosion. The 6 VDC battery will be charging at an excessive rate. The 12 VDC battery will be discharging at a rapid rate. Both will get hot. Both will liberate hydrogen (assuming lead acid chemistry). Both could explode!

Regards,

APD
• At , don't you need to take the inverse of that expression to get the equivalent resistance of the 2 resistors in parallel?
• R1R2/(R1+R2) is actually already the inverse of the expression 1/R total.
• Sorry, I'm not clear about the section at 3.06-3.26 when he talks about nodes (in orange). I understand why all three have the same voltage but he then says the ones on the right are 11 volts lower. Why 'lower'?
• They are lower because they are on the negative side of the battery. The bigger side of the battery ie. the node drawn longer is 11V but the negative side of the battery is 0V and the current flows from an area with high voltage to low voltage.
• At , how did he know that the total voltage, or the two batteries together, would still equate to 11V? I'm confused. Won't they add up or something? I don't have the intuition to understand this right now. Can someone please explain?
• Two batteries connected in parallel have the same voltage as one battery, but twice the capacity to deliver current.

Two batteries connected in series (like in a flashlight) have sum of the voltage of the two batteries. Two AA batteries (1.5v) in series produces 3v from end to end.

Batteries in parallel are kind of like two big bricks standing up side-by-side. The top of one brick is about one foot off the floor. That corresponds to a voltage of "1 foot". If you put an identical brick next to it, the top is still one foot off the floor (so it is the same voltage). But now that there's two bricks you can put twice as much weight on top of them before they crumble.
• Why is it that you can draw the imaginary wire between the two batteries to make them one big battery? Why doesn’t current flow through it?
• These batteries are treated as ideal voltage sources. This means that they will source whatever current is pulled by a load and sink any current flows in to keep their output voltage at 11V.
• What happens if two batteries of different voltage are connected in parallel? In series they would add up right?
• Hello Ayushi,

Keep in mind that batteries are NOT ideal voltage sources. But the results are similar.

Please forgive the crude nature of the video. I'm still trying to figure out how to use the tools...

Regards,

APD
• So 2 parallel batteries with 11 Volts produce the same amount of current as a single 11V batterie? I would get same results with just one batterie...
• The 2 parallel batteries of 11 Volts produce the same amount of voltage as a single 11V battery. The two batteries have twice the amount of stored energy as one battery, so as a pair they will last longer. The amount of current provided by both the 1-battery or 2-battery setup is not determined by the batteries, but rather by the components the batteries are connected to (using Ohm's Law on the resistors in the circuit). The batteries maintain 11V on their terminals, by providing whatever current is "demanded" by the connected components. If the circuit demands a lot of current, the single battery will run out of energy and die sooner than the double battery setup.
• are the batteries connected in parallel always at the same voltage?if they are then why cant the batteries in parallel be at diff. voltages? if these batteries were connected in series they would have been additive right?
• Hello Sidra,

If you accidentally connect batteries of different voltages together your should run away especially if the batteries are large there is a real risk of explosion!

In this case there will be an uncontrolled current flow as the high voltage battery discharges and the low voltage battery charges.

I made this video to help explain the situation:

Regards,

APD
• What would happen if the voltage of the batteries is different?
• Hello Ananya,

Congratulations on posting your first question to KA!

If the voltages are different then a current will flow between the batteries. Depending on the batteries this could lead to a spectacular explosion!

Observe that many mathematical tools are applied in this situation including Kirchhoff, Thevenin, and Ohm. Know that It take time to learn the tools and how to apply them. Have fun experimenting.

Best wishes,

APD
(1 vote)
• If I apply kirchoffs' voltage law into the loop made up by two batteries and two smaller resistors, the voltage around the loop cannot add up to zero by the ordinary precedure. Why is that?
• Hello Ruohua,

KVL should hold even if the batteries have different voltages.