In the electric field of a point charge $\mathrm{q}$, a certain charge is carried from point $\mathrm{A}$ to $\mathrm{B}$, $\mathrm{C}$, $\mathrm{D}$ and $\mathrm{E}$. Then the work done

In the circuit shown below, a student performing Ohm's law experiment accidentally puts the voltmeter and the ammeter as shown in the circuit below; the reading in the voltmeter will be close to

In a conductor, if the number of conduction electrons per unit volume is $8.5\times {10}^{28}{\mathrm{m}}^{-3}$ and mean free time is $25f\mathrm{s}$ (femtosecond), its approximate resistivity is: $\left({\mathrm{m}}_{\mathrm{e}}=9.1\times {10}^{-31}\mathrm{k}\mathrm{g}\right)$

Model a torch battery of length $l$ to be made up of a thin cylindrical bar of radius $a$ and a concentric thin cylindrical shell of radius $b$ filled in between with an electrolyte of resistivity $\rho$ (see figure). If the battery is connected to a resistance of value $R$, the maximum Joule heating in $R$ will take place for :

Find the potential difference between $a$ and $b$, as shown in the below circuit.

In the figure shown, what is the current (in ampere) drawn from the battery? You are given:
$R_1=15 \mathrm{\Omega }\mathrm{ }, R_2=10 \mathrm{\Omega }\mathrm{ }, R_3=20 \mathrm{\Omega }\mathrm{ }, R_4=5 \mathrm{\Omega },\mathrm{ }{R}_5=25 \mathrm{\Omega },\mathrm{ }{R}_6=30 \mathrm{\Omega },\mathrm{ }E=15 \mathrm{V}$