Question

You measured the voltage across the battery terminals both for the circuit connected to the battery and for no circuit connected to the battery. The difference between these two readings is due to internal resistance of the battery holder. Determine the internal resistance of the battery holder treating this resistance as being in series with the equivalent resistance of the circuit when the circuit is connected.

Answer 1

Answer:

$Ri=\frac{Vs}{I} - R$

Explanation:

The measure of the voltage across the battery for no circuit connected to the baterry is the voltage of the ideal voltage source (without internal resistance) because there isn't current flowing therefore the voltage of the internal resistance is zero.

Let Vs represent the open-circuit voltage.

The measure of the voltage across the battery terminals for the circuit connected to the baterry is the voltage of the connected resistance (Let R represent it)

Let Vr represent the connected circuit voltage.

Let Ri represent the internal resistance.

Applying Kirchhoff's Voltage Law for the circuit connected to the batery:

Vs=Vi+Vr (I)

where Vi is the voltage of the internal resistance and Vr is the voltage of the load (R)

The voltage of the load is:

Vr=IR

You can obtain the value of the current I because Vr and R are known.

I=Vr/R

Which is the same current across the internal resistance because the connection is in series.

The equation (I) can be written as:

Vs=I(Ri+R)

Therefore you can solve it for Ri, because Vs, I and R are known.

Dividing by I and subtracting R:

Ri = Vs/I - R