One end of a nichrome wire of length $2L$ and cross-sectional area $A$ is attached to an end of another nichrome wire of length $L$ and cross-sectional area $2A$. If the free end of the longer wire is at an electric potential of $8.0$ $\mathrm{V}$ and the free end of the shorter wire is at an electric potential of the $1.0 \mathrm{V}$ , the potential at the junction of the two wires is approximately-

An electric cable having a resistance $R$ delivers $11 \mathrm{kW}$ of power at $220 \mathrm{V}$ to a factory. If the efficiency of transmission is $91\%$, then what is the value of $R$?

A battery of e.m.f $12 \mathrm{V}$ and internal resistance $0.5 \mathrm{\Omega }$ is charged by a battery charger which supplies a $132 \mathrm{V}$ d.c. supply using a series resistance of $11.5 \mathrm{\Omega }$. What is the terminal voltage of the battery during charging?

A heating coil of resistance $100 \mathrm{\Omega }$ takes $100 \mathrm{s}$ to boil certain amount of water. If a similar heating coil is connected in series with the heating coil, then the time required to boil the water is $t_{\mathrm{s}}$, while $t_{\mathrm{p}}$ time is required to boil the same amount of water if the coils are connected in parallel. What will be $\frac{t_{\mathrm{s}}}{t_{\mathrm{p}}}$?

Five identical resistors, each of resistance $1 \mathrm{\Omega }$, are initially arranged as shown in the figure by clear lines. If two similar resistances are added as shown by the dashed lines, then change in resistance in final and initial arrangements is,