Electric Current

The current density in a cylindrical wire of radius $r=4.0 \mathrm{mm}$ is $1.0\times {10}^6{ \mathrm{A}}^2{ \mathrm{m}}^2$. The current through the outer portion of the wire between radial distances $\frac{r}{2}$ and $r$ is $x\pi \mathrm{A}$; where $x$ is

The current density in a cylindrical wire of radius $4 \mathrm{mm}$ is $4\times {10}^6 \mathrm{A} {\mathrm{m}}^{-2}$. The current through the outer portion of the wire between radial distances $\frac{R}{2}$ and $R$ is _____ $\pi \mathrm{A}$.

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

A straight conductor carries a steady current. Assume in it all free electrons in the conductor move with same drift velocity $V$. $A$ and $B$ are two observers in a straight line XY parallel to the conductor. $A$ is stationary, $B$ moves along $XY$ with a velocity $V$ in the direction of free electrons

A medium is separated from other medium of refractive index ${\mu }_0$ by $x-z$ plane. Refractive index of the medium varies as $\mu ={\mu }_0-{\mu }_1\mathrm{y}+{\mu }_2{\mathrm{y}}^2$, choose the CORRECT statement(s). A ray is incident from the other medium to this medium ($\left({\mu }_0,{\mu }_1 \& {\mu }_2\right)$are positive)

A charged particle of mass '$m$' and charge '$q$' is projected on a rough horizontal $X-Y$ plane ($z$-axis is vertically upwards), both electric and magnetic fields are acting in the region and given by $\overrightarrow{E}=-E_{0}k$ and $\overrightarrow{B}=-B_{0}k$ respectively. The particle enters into the field at $\left(a_0,0,0\right)$ with velocity $\overrightarrow{v}=v_0\hat{\mathrm{j}}$. The particle starts moving in a curved path on the plane. If coefficient of friction between the particle and the plane is $\mu$, then (take gravitational acceleration $g\left(-\hat{k}\right){\mathrm{ms}}^{-2}$)

A conductor which is required to retain its charge for a long time should 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 

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 _____ in SI unit.

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.]

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 $76.3 \mathrm{cm}.$ When a resistor of $9.5 \mathrm{\Omega }$ is used in the external circuit of the cell, the balance point shifts to $64.8 \mathrm{cm}$ length of the potentiometer wire. Fine the internal resistance of the cell (in $\mathrm{\Omega }$) correct to the nearest integer.

The circuit diagram given in the figure shows the experimental setup for the measurement of unknown resistance by using a meter bridge. The wire connected between the points $P \& Q$ has non-uniform resistance such that resistance per unit length varies directly as the distance from the point $P.$ Null point is obtained with the jockey $J$ with $R_1$ and $R_2$ in the given position. On interchanging the positions $R_1$ and $R_2$ in the gaps the jockey has to be displaced through a distance $\Delta$ from the previous position along the wire to establish the null point. If the ratio of $\frac{R_1}{R_2}=3,$ find the value of $\Delta$ (in $cm$). Ignore any end corrections. [Take $\sqrt{3}=1.7$]

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,