If the discharged battery is charged by an external emf source, is the terminal voltage of the battery during charging greater or less than $12 \mathrm{V}$ ?

A variable rheostat of $2 \mathrm{K\Omega }$, Fig. is used to control the p.d. across a $500 \mathrm{\Omega }$ load ${\mathrm{R}}_{\mathrm{L}}$. If the resistance $\mathrm{A} \mathrm{B}$ is $500 \mathrm{\Omega }$, what is p.d. across ${\mathrm{R}}_{\mathrm{L}}?$ If ${\mathrm{R}}_{\mathrm{L}}$ is removed, what should be the resistance $\mathrm{B} \mathrm{C}$ to get $40 \mathrm{V}$ between $\mathrm{B}$ and $\mathrm{C}$.

In the given network of Fig. $5.133,{\mathrm{R}}_1=100$$\mathrm{\Omega },{\mathrm{R}}_2={\mathrm{R}}_3=50{\mathrm{\Omega R}}_4=$$75 \mathrm{\Omega }$ and $\mathrm{E}=6.0 \mathrm{V}$ Find the currents in each resistor.

Calculate the equivalent resistance between the points $\mathrm{A}$ and $\mathrm{B}$ of the following network of conductors in Fig.