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33)Seriously, this one is a doozy the wording is not very nice, to be honest, and it makes the question rather confusing.
What it actually asks for (as far as I can tell) are the variables required to find the different between OPEN circuit voltage and CLOSED circuit voltage. In other words, the difference between the potential difference measured when the circuit is OPEN and when it is fully connected with an external resistor.
(I thought it spoke about the normal decrease in voltage with running duration, which can be expected as a battery runs down. My mistake!)
A Google Images search for "internal external resistance" provides some very clear images, and i'm using the attached one for reference.
When the circuit is open, no current flows through the battery, and the initial reading the equivalent to the EMF of the battery; no energy is lost per second to heat in the internal resistance, so it is equal to the EMF.
Let's write this down as V.
Once the circuit is connected as above, a current indeed does flow through all components, and a potential difference is maintained across each too. However, since the battery consists of an internal resistance (this internal resistance is NEVER separate from the battery; it can be considered as such, but the battery consists both of the cells and the internal resistance), there is a drop in potential across this internal resistance before the current even leaves the battery. Thus, the potential difference across the terminals of the battery drop.
Applying Kirchoff's Second Law while moving from B to A, what we get is (V is still the EMF, r(internal) is the internal resistance):
(Potential at A) + V - i * r(internal) = (Potential at B)
All this says is that the potential at A is one thing, it changes by so and so amount, as a result of which is becomes another value, the Potential at B.
So, since the Potential Difference is the (Potential at B) - (Potential at A), we have:
PD = V - i * r(internal)
Thus, the drop in potential is
V - (V- i * r(internal)) = i * r(internal)
The change is negative, but the decrease is positive, so the signs change there. Therefore, all you need to find the drop in potential are the final current, and the internal resistance of the battery = C
What it actually asks for (as far as I can tell) are the variables required to find the different between OPEN circuit voltage and CLOSED circuit voltage. In other words, the difference between the potential difference measured when the circuit is OPEN and when it is fully connected with an external resistor.
(I thought it spoke about the normal decrease in voltage with running duration, which can be expected as a battery runs down. My mistake!)
A Google Images search for "internal external resistance" provides some very clear images, and i'm using the attached one for reference.
When the circuit is open, no current flows through the battery, and the initial reading the equivalent to the EMF of the battery; no energy is lost per second to heat in the internal resistance, so it is equal to the EMF.
Let's write this down as V.
Once the circuit is connected as above, a current indeed does flow through all components, and a potential difference is maintained across each too. However, since the battery consists of an internal resistance (this internal resistance is NEVER separate from the battery; it can be considered as such, but the battery consists both of the cells and the internal resistance), there is a drop in potential across this internal resistance before the current even leaves the battery. Thus, the potential difference across the terminals of the battery drop.
Applying Kirchoff's Second Law while moving from B to A, what we get is (V is still the EMF, r(internal) is the internal resistance):
(Potential at A) + V - i * r(internal) = (Potential at B)
All this says is that the potential at A is one thing, it changes by so and so amount, as a result of which is becomes another value, the Potential at B.
So, since the Potential Difference is the (Potential at B) - (Potential at A), we have:
PD = V - i * r(internal)
Thus, the drop in potential is
V - (V- i * r(internal)) = i * r(internal)
The change is negative, but the decrease is positive, so the signs change there. Therefore, all you need to find the drop in potential are the final current, and the internal resistance of the battery = C