Electric Current

In hydrogen discharge tube, it is observed that through a given cross-section $5\times {10}^{16}$ electrons are moving from right to left and $5\times {10}^{16}$ protons are moving from left to right per second. The current(in $\mathrm{mA}$) in the discharge tube will be

Current flowing through a wire depends on time as $I=3t^2+2t+5.$ The charge flowing through the cross-section of the wire in time $t=0$ to $t=2 \mathrm{s}$ is 

The amount of charge $Q$ passed in time $t$ through a cross section of a wire is $Q=5t^2+3t+1.$ The value of current at time $t=5s$ is 

Current is flowing with a current density $J=480 \mathrm{A} \mathrm{c}{\mathrm{m}}^{-2}$ in a copper wire. Assuming that each copper atom contributes one free electron and given that

Avogadro number $=6.0\times {10}^{23}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{ }{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}$

Density of copper $=9.0\mathrm{g}\mathrm{ }{\mathrm{c}\mathrm{m}}^{-3}$

Atomic weight of copper $=64\mathrm{g}\mathrm{ }{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}$

The drift velocity of electrons is

A current of $2 \mathrm{A}$ is established in a circuit containing an aluminium resistor of length $30 \mathrm{cm}$. If the area of cross-section of the resistor is $0.003 {\mathrm{cm}}^2$ at a point P.The current density at that point will be :

A cylindrical conductor has length $l$ and area of cross-section $A.$ Its conductivity changes with distance $\left(x\right)$ from one of its ends as $\sigma ={\sigma }_0\frac{l}{x}$ [${\sigma }_0$ is a constant]. The electric field inside the conductor as a function of $x$ is $\frac{k}{10} \mathrm{V} {\mathrm{m}}^{-1}$  when a cell of emf $V$ is connected across the ends. Find $k$. [Given that $l=10 \mathrm{m}, x=2 \mathrm{m},\mathit{ }V=10$ Volt.]

A steady current $I$ is set up in a wire whose cross-sectional area decreases in the direction of the flow of the current. Then, as we examine the narrowing region

Number of electrons passes through a wire in $2$ minutes is $2.25\times {10}^y$, if current passing through the wire is $300 \mathrm{mA}$. Find the value of $y$.

The current through an element is shown in the figure. Determine the total charge that passes through the element after  $t= 2 \mathrm{s}$ in Coulombs.

In the circuit element given here, if the potential at point $B\text{,} V_{\mathrm{B}}=0\text{,}$ then the potentials of $A$ and $D$ are given as,

The current through an element is shown in the figure. Determine the total charge that passes through the element after  $t= 2 \mathrm{s}$ in Coulombs.

The current through an element is shown in the figure. Determine the total charge that has passed through the element at $t=0 \mathrm{s}$ in Coulombs.

Number of electrons passes through a wire in $2$ minutes is $2.25\times {10}^y$, if current passing through the wire is $300 \mathrm{mA}$. Find the value of $y$.

A source of e.m.f. $E = 15 \mathrm{V}$and having negligible internal resistance is connected to a variable resistance so that the current in the circuit increases with time as $i = (1.2 t + 3).$ Then, the total charge that will flow in first five second will be

A cylindrical solid rod of length $L$ and radius $a$ is connected across a source of emf $V$ and negligible internal resistance as shown in the figure. The resistivity of the rod at point $P$ at a distance $x$ from the left end is given by $\rho =bx$ (where $b$ is a positive constant). Find the electric field at point $P$.

A fully discharged battery (emf$=12 \mathrm{V}$, capacity$=60 \mathrm{Ah}$) is connected with a charging device that can supply the battery a steady current, $i=3 \mathrm{A}$. The battery is connected to charging device for $90 \min$. Final charging level of battery (in percentage) is,

A sphere of radius $r$ is at a potential $\mathrm{V}$ and is immersed in a conducting medium of conductivity $\sigma .$ Find the current flowing from sphere to infinity.

A current $2 \mathrm{A}$ flows through a $2 \mathrm{\Omega }$ resistor when connected across a battery. The same battery supplied a current $0.5 \mathrm{A}$ when connected across a $9 \mathrm{\Omega }$ resistor. The internal resistance of the battery is

In a region ${10}^{19}\alpha$ particles and ${10}^{19}$ protons move to the left, while ${10}^{19}$ electrons move to the right per sec. find $\frac{\Delta \mathrm{q}}{\Delta \mathrm{t}}:-$

The current density varies with radial distance $r$ as $J=a{r}^2,$ in a cylindrical wire of radius $R\mathit{.}$ The current passing through the wire between radial distance $R/3$ and $R/2$ is,