Electric Current, Drift Velocity & Current Density

In the circuit shown charge q varies with time t as $q = t^{2} - 5$, where q is in coulomb and t is in second. At time $t = 3$ second, voltage $V_{AB}$ in volt will be

A cylindrical conductor of length 2 m and area of cross-section $0.2\text{ mm}^{2}$ carries an electric current of 1.6 A when its ends are connected to a 2 V battery. Mobility of electrons in the conductor is $\alpha \times 10^{-3}\text{ m}^{2}\text{/V s}$. The value of $\alpha$ is:

(electron concentration $= 5 \times 10^{28}\text{ /m}^{3}$ and electron charge $= 1.6 \times 10^{-19}\text{ C}$)

Current passing through a wire as function of time is given as $I(t) = 0.02t + 0.01\text{ A}$. The charge that will flow through the wire from $t = 1\text{ s}$ to $t = 2\text{ s}$ is

The number of electrons flowing per second in the filament of a $110\text{ W}$ bulb operating at $220\text{ V}$ is: (Given $\text{e} = 1.6 \times 10^{-19}\text{ C}$)

The electric current through a wire varies with time as $I = I_0 + \beta t$, where $I_0 = 20\text{ A}$ and $\beta = 3\text{ A/s}$. The amount of electric charge crossed through a section of the wire in $20\text{ s}$ is:

The current in a conductor is expressed as $I = 3t^{2} + 4t^{3}$, where $I$ is in Ampere and $t$ is in second. The amount of electric charge that flows through a section of the conductor during $t = 1\text{ s}$ to $t = 2\text{ s}$ is __________ C.

A uniform wire of diameter $d$ carries a current of $100\text{ mA}$ when the mean drift velocity of electrons in the wire is $v$. For a wire of diameter $\frac{d}{2}$ of the same material to carry a current of $200\text{ mA}$, the mean drift velocity of electrons in the wire is

A copper wire of radius $1\text{ mm}$ contains $10^{22}$ free electrons per cubic metre. The drift velocity for free electrons when $10\text{ A}$ current flows through the wire will be (Given, charge on electron $= 1.6 \times 10^{-19}\text{ C}$):

In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor

The number density of free electrons in copper is nearly $8 \times 10^{28}\text{ m}^{-3}$. A copper wire has its area of cross section $= 2 \times 10^{-6}\text{ m}^{2}$ and is carrying a current of $3.2\text{ A}$. The drift speed of the electrons is ___________ $\times 10^{-6}\text{ m s}^{-1}$

A current of $2\text{ A}$ flows through a wire of cross-sectional area $25.0\text{ mm}^{2}$. The number of free electrons in a cubic meter are $2.0 \times 10^{28}$. The drift velocity of the electrons is __________ $\times 10^{-6}\text{ m s}^{-1}$ (given, charge on electron $= 1.6 \times 10^{-19}\text{ C}$ ).

The charge flowing in a conductor changes with time as $Q(t) = \alpha t - \beta t^{2} + \gamma t^{3}$. Where $\alpha, \beta$ and $\gamma$ are constants. Minimum value of current is:

The drift velocity of electrons for a conductor connected in an electrical circuit is $V_{d}$. The conductor is now replaced by another conductor with same material and same length but double the area of cross section. The applied voltage remains same. The new drift velocity of electrons will be

(A) The drift velocity of electrons decreases with the increase in the temperature of conductor. (B) The drift velocity is inversely proportional to the area of cross-section of given conductor. (C) The drift velocity does not depend on the applied potential difference to the conductor. (D) The drift velocity of electron is inversely proportional to the length of the conductor. (E) The drift velocity increases with the increase in the temperature of conductor. Choose the correct answer from the options given below:

A copper wire of length 10 m and radius $\left(\frac{10^{-2}}{\sqrt{\pi}}\right)$ m has electrical resistance of 10 $\Omega$. The current density in the wire for an electric field strength of 10 (V/m) is

A $1\text{ m}$ long copper wire carries a current of $1\text{ A}$. If the cross section of the wire is $2.0\text{ mm}^{2}$ and the resistivity of copper is $1.7 \times 10^{-8}\ \Omega\text{ m}$, the force experienced by moving electron in the wire is ____________ $\times 10^{-23}\text{ N}$.

(charge on electron $= 1.6 \times 10^{-19}\text{ C}$)

The current density in a cylindrical wire of radius r = 4.0 mm is 1.0 $\times$ 106 A/m2. The current through the outer portion of the wire between radial distances $\frac{r}{2}$ and r is x$\pi$ A; where x is __________.

The current density in a cylindrical wire of radius 4 mm is 4 $\times$ 106 Am${}^{-2}$. The current through the outer portion of the wire between radial distances $\frac{R}{2}$ and R is ____________ $\pi$ A.

A current through a wire depends on time as

i = $\alpha$0t + $\beta$t2

where $\alpha$0 = 20 A/s and $\beta$ = 8 As${}^{-2}$. Find the charge crossed through a section of the wire in 15 s.

A current of 10A exists in a wire of cross-sectional area of 5 mm2 with a drift velocity of 2 $\times$ 10$-$3 ms${}^{-1}$. The number of free electrons in each cubic meter of the wire is ___________.

Column - I gives certain physical terms associated with flow of current through a metallic

conductor. Column-II gives some mathematical relations involving electrical quantities. Match

column-I and column-II with appropriate relations.

In the given figure, a battery of emf E is connected across a conductor PQ of length 'l' and different area of cross-sections having radii r1 and r2 (r2 < r1).

Choose the correct option as one moves from P to Q:

A conducting wire of length 'l', area of cross-section A and electric resistivity $\rho$ is connected between the terminals of a battery. A potential difference V is developed between its ends, causing an electric current.

If the length of the wire of the same material is doubled and the area of cross-section is halved, the resultant current would be:

A current of 5 A is passing through a non-linear magnesium wire of cross-section 0.04 m2. At every point the direction of current density is at an angle of 60$^\circ$ with the unit vector of area of cross- section. The magnitude of electric field at every point of the conductor is:

(Resistivity of magnesium $\rho$ = 44 $\times$ 10$-$8 $\Omega$m)

A cylindrical wire of radius 0.5 mm and conductivity 5 $\times$ 107 S/m is subjected to an electric field of 10 mV/m. The expected value of current in the wire will be x3$\pi$ mA. The value of x is _________.

A charged particle having drift velocity 7.5 $\times$ 10-4 ms-1 in an electric field of 3 $\times$ 10-10 Vm-1 has a mobility in m2 V-1s-1 of:

Drift speed of electrons, when 1.5 A of current flows in a copper wire of cross section 5 mm2, is $v$. If the electron density in copper is 9 $\times$ 1028/m3 the value of $v$. in mm/s is close to (Take charge of electron to be = 1.6 $\times$ 10$-$19C)

In a conductor, if the number of conduction electrons per unit volume is 8.5 × 1028 m–3 and mean free time is 25ƒs (femto second), it's approximate resistivity is :-

(me = 9.1 × 10–31 kg)

A current of 5 A passes through a copper conductor (resistivity = 1.7 × 10–8 $\Omega$m) of radius of cross- section 5 mm. Find the mobility of the charges if their drift velocity is 1.1 × 10–3 m/s.

A copper rod of cross-sectional area A carries a uniform current I through it. At temperature T, if the volume charge density of the rod is $\rho$, how long will the charges take to travel a distance d?

Across a metallic conductor of non-uniform cross section a constant potential difference is applied. The quantity which remains constant along the conductor is

When $5\text{ V}$ potential difference is applied across a wire of length $0.1\text{ m},$ the drift speed of electrons is $2.5 \times 10^{-4}\text{ m s}^{-1}.$ If the electron density in the wire is $8 \times 10^{28}\text{ m}^{-3},$ the resistivity of the material is close to:

$-$8

The mean free path of electrons in a metal is 4 $\times$ 10 m. The electric field which can give on an average 2 eV energy to an electron in the metal will be in units V/m

A flow of $10^{7}$ electrons per second in a conducting wire constitutes a current of

The velocity of charge carriers of current (about 1 ampere) in a metal under normal conditions is of the order of