Cells, EMF, Internal Resistance

The figure shows a $2.0 \mathrm{V}$ potentiometer used for the determination of internal resistance of a $1.5 \mathrm{V}$ cell. The balance point of the cell in open circuit is $76.3 \mathrm{c}\mathrm{m}$. When a resistor of $9.5 \mathrm{\Omega }$ is used in the external circuit of the cell, the balance point shifts to $64.8 \mathrm{c}\mathrm{m}$ length of the potentiometer wire. Determine the internal resistance of the cell.

Determine the current drawn from a $12 \mathrm{V}$ supply with internal resistance $0.5 \mathrm{\Omega }$ by the infinite network shown below. Each resistor has $1 \mathrm{\Omega }$ resistance

Determine the equivalent resistance of networks shown below.

A secondary cell after long use has an emf of $1.9 \mathrm{V}$ and a large internal resistance of $380 \mathrm{\Omega }$. What maximum current can be drawn from the cell? Could the cell drive the starting motor of a car?

A storage battery of emf $8.0 \mathrm{V}$ and internal resistance $0.5 \mathrm{\Omega }$ is being charged by a $120 \mathrm{V}$ dc supply using a series resistor of $15.5 \mathrm{\Omega }.$ What is the terminal voltage of the battery during charging? What is the purpose of having a series resistor in the charging circuit?