# Batteries in Parallel Arrangement

• B
Hi pf,

Consider a D.C. circuit with a 5V battery and a 5 ohm resistor which will draw a current of 1A. If we ignore internal resistance then adding another battery in parallel will not change the current through the resistance (V=IR). What will happen is that each battery gets 0.5A each now and they last longer (twice as long). My question is what happens in a situation where the second battery you add in parallel is not the same. Keep the original situation above the same but now add a second battery in parallel which is 10V. Still ignoring internal resistance what happens to the voltage across the resistor and the current through it? Will the voltage across the resistor fluctuate since some of the Coulombs of charge will deliver 10J whilst others will deliver 5J?

Thanks.

davenn
Gold Member
2021 Award
Still ignoring internal resistance what happens to the voltage across the resistor and the current through it?

and before you consider that

consider this

My question is what happens in a situation where the second battery you add in parallel is not the same. Keep the original situation above the same but now add a second battery in parallel which is 10V.

how do you think the 5V battery is going to react to an extra 5V across its terminals ?

Dave

• Jimmy87
QuantumQuest
Gold Member
Hi pf,

Consider a D.C. circuit with a 5V battery and a 5 ohm resistor which will draw a current of 1A. If we ignore internal resistance then adding another battery in parallel will not change the current through the resistance (V=IR). What will happen is that each battery gets 0.5A each now and they last longer (twice as long). My question is what happens in a situation where the second battery you add in parallel is not the same. Keep the original situation above the same but now add a second battery in parallel which is 10V. Still ignoring internal resistance what happens to the voltage across the resistor and the current through it? Will the voltage across the resistor fluctuate since some of the Coulombs of charge will deliver 10J whilst others will deliver 5J?

Thanks.

The battery with the higher EMF will supply voltage to the lower EMF one, until they get to the same voltage. Now, the whole thing depends on the internal resistances of the batteries and the current that flows there, can be calculated using Ohm's law. Because current will be somewhat high, it can potentially damage one or both batteries. If internal resistance is very low, so much the worse for the batteries.

• Jimmy87
The battery with the higher EMF will supply voltage to the lower EMF one, until they get to the same voltage. Now, the whole thing depends on the internal resistances of the batteries and the current that flows there, can be calculated using Ohm's law. Because current will be somewhat high, it can potentially damage one or both batteries. If internal resistance is very low, so much the worse for the batteries.

If we ignore internal resistance then in this case what will the net voltage of a 5V and 10V be? 5V?

davenn
Gold Member
2021 Award
Because current will be somewhat high, it can potentially damage one or both batteries. If internal resistance is very low, so much the worse for the batteries.

QQ I was hoping that the OP would think about it and come up with some comments instead of you or some one else doing it for him

please consider your responses when you see an OP has been asked a Q ... don't give answers till the OP has at least tried to respond

thanks lots
Dave

Last edited:
• phinds, Fervent Freyja and QuantumQuest
QuantumQuest
Gold Member
QQ I was hoping that the OP would think about it and cone up with some comments instead of you or some one else doing it for him

please consider your responses when you see an OP has been asked a Q ... don't give answers till the OP has at least tried to respond

thanks lots
Dave

Yes , I usually don't give ready-to-go answers. My apologies for that.

• davenn
QQ I was hoping that the OP would think about it and come up with some comments instead of you or some one else doing it for him

please consider your responses when you see an OP has been asked a Q ... don't give answers till the OP has at least tried to respond

thanks lots
Dave

So would the net voltage of a 10V and 5V battery in parallel just simply be 5V?

cnh1995
Homework Helper
Gold Member
So would the net voltage of a 10V and 5V battery in parallel just simply be 5V?
You need to consider the internal resistances now. If you consider the batteries to be ideal, the situaltion becomes invalid. It is invalid to connect two ideal voltage sources in parallel and two ideal current sources in series.

• davenn
Delta2
Homework Helper
Gold Member
You need to consider the internal resistances now. If you consider the batteries to be ideal, the situaltion becomes invalid. It is invalid to connect two ideal voltage sources in parallel and two ideal current sources in series.

By invalid you mean that the current (through each voltage source) becomes infinite? Cause that is what we ll get if we try to find the current by assuming internal resistance r(same for both sources) and then taking the limit r->0.

• CWatters
sophiecentaur
Gold Member
So would the net voltage of a 10V and 5V battery in parallel just simply be 5V?
It would depend entirely on the particular batteries being used. The above posts have pointed out that you cannot consider two 'ideal' batteries.
Try this exercise for yourself:
Two batteries with different voltages (emf) and different internal resistances. 5V with 10Ω and 10V with 100Ω. Ignoring the practical possibility of frying one of the batteries if they were 'real', look at the resulting terminal volts when they're in parallel. Then swap the 10Ω and 100Ω resistances and look at the terminal Volts. Different answers. So there's no definitive answer to your question.
PS an ideal Voltage source will maintain the voltage across it whether that involves sinking or sourcing current. The internal resistances could be getting pretty hot.

cnh1995
Homework Helper
Gold Member
By invalid you mean that the current (through each voltage source) becomes infinite? Cause that is what we ll get if we try to find the current by assuming internal resistance r(same for both sources) and then taking the limit r->0.
By invalid, I mean indefinite, like 0/0. If two batteries of 5V and 10V are connected across the same resistor R and internal resistances are assumed to be zero, voltage across R can't be defined since both the sources will try to maintain their respective voltages across R. Obviously, the voltage across R can't be 5V and 10V at the same time. It is an invalid condition in network theory. Internal resistances of the batteries must be considered in this situation.

• Delta2
CWatters
Homework Helper
Gold Member
Rules...

Never short circuit an ideal voltage source.
Never open circuit an ideal current source.
Never connect ideal voltage sources in parallel (unless same voltage)
Never connect ideal current sources in series (unless same current)
Always leave your multimeter set on Volts.

• cnh1995