Current Electricity

A metal wire of cross-sectional area $0.5$ mm$^2$ and length $100$ m is connected across a battery of e.m.f. $2$ V and internal resistance $1\ \Omega$. The density, atomic mass and electrical conductivity of the metal are $6.35\times10^3$ kg m$^{-3}$, $63.5$ gm/mole and $2\times10^8$ mho m$^{-1}$, respectively. Assuming one conduction electron per atom of the metal, the drift velocity (in mm s$^{-1}$) of the electrons in the wire is:
[Take Avogadro's number as $6\times10^{23}$ and charge of the electron as $1.6\times10^{-19}$ C.]

As shown in the figure, the resistance of a galvanometer $G$ can be found by the half-deflection method. Here the resistance $R_2$ is adjusted such that when the key $K$ is closed the deflection in the galvanometer becomes half of the value as compared to when $K$ is open. Half-deflection is obtained at $R_2=4\ \Omega$ and thus the galvanometer resistance is found to be $6\ \Omega$. In this half-deflection condition the current (in mA) through the resistor $R_1$ is:

When a coil is placed in a time dependent magnetic field the power dissipated in it is $P$. The number of turns, area of the coil and radius of the coil wire are $N$, $A$ and $r$ respectively. For a second coils number of turns, area of the coil and radius of the coil wire are $2N$, $2A$ and $3r$ respectively. When the first coil is replaced with second coil the power dissipated in it is $\sqrt2\,\alpha P$. The value of $\alpha$ is ________.

Two resistors of 200 Ω and 400 Ω are connected in series with a battery of 100 V. A bulb rated at 200 V, 100 W is connected across the 400 Ω resistance. The potential drop across the bulb is ________ V.

A voltmeter with internal resistance of $x$ Ω can be used to measure upto 20 V. In order to increase its measuring range to 30 V, the required modification is to ________.

The voltage and the current between $A$ and $B$ points shown in the circuit are ________.

Refer to the figure given below. The values of $I_1$, $I_2$ and $I_3$ are ________.

Refer to the figure given below, current between terminals $A$ and $B$ is ________ A.

Under steady state condition the potential difference across the capacitor in the circuit is ________ V.

When an external resistance of 5 Ω is connected across terminals of a cell, a current of 0.25 A flows through it. When the 5 Ω resistor is replaced by a 2 Ω resistor, a current of 0.5 A flows through it. The internal resistance of the cell is ________ Ω.

Refer to the circuit diagram given below. The heat generated across the 6 Ω resistance in 100 second is $\dfrac\alpha{100}$ J. The value of $\alpha$ is ________. (Nearest integer)

A moving coil of galvanometer when shunted with 2 Ω resistance gives a full scale deflection for a current of 500 mA. When a resistance of 470 Ω is connected in series it gives a full scale deflection for 10 V potential applied on it. The value of resistance of galvanometer coil is ________ Ω.

Two cells of emfs 1 V and 2 V and internal resistance 2 Ω and 1 Ω, respectively connected in parallel, gave a current of 1 A through an external resistance. If the polarity of one cell is reversed, then value of current through the external resistance will be $\dfrac\alpha5$ A. The value of $\alpha$ is ________.

A parallel plate capacitor is having separation between plates 0.885 mm. It has a capacitance of 1 μF when the space between the plates is filled with an insulating material of resistivity $1\times10^{13}$ Ωm and resistance $17.7\times10^{14}$ Ω. Relative permittivity of the insulating material is $\alpha\times10^7$. The value of $\alpha$ is ________.

(Take permittivity of free space $=8.85\times10^{-12}$ F/m)

The stored charge in the capacitor in steady state of the following circuit is ________ μC.

In a circuit shown in the figure, the capacitor $C$ is initially uncharged and the key $K$ is open. In this condition, a current of 1 A flows through the $1\,\Omega$ resistor. The key is closed at time $t = t_0$. Which of the following statement(s) is(are) correct?

[Given: $e^{-1} = 0.36$]

The figure shows a circuit having eight resistances of $1\ \Omega$ each, labelled $R_1$ to $R_8$, and two ideal batteries with voltages $\mathcal E_1 = 12$ V and $\mathcal E_2 = 6$ V.

Which of the following statement(s) is(are) correct?

Two resistances $R_1 = X\ \Omega$ and $R_2 = 1\ \Omega$ are connected to a wire $AB$ of uniform resistivity, as shown in the figure. The radius of the wire varies linearly along its axis from 0.2 mm at $A$ to 1 mm at $B$. A galvanometer (G) connected to the center of the wire, 50 cm from each end along its axis, shows zero deflection when $A$ and $B$ are connected to a battery. The value of $X$ is _____.

In Circuit-1 and Circuit-2 shown in the figures, $R_1 = 1\ \Omega$, $R_2 = 2\ \Omega$ and $R_3 = 3\ \Omega$.
$P_1$ and $P_2$ are the power dissipations in Circuit-1 and Circuit-2 when the switches $S_1$ and $S_2$ are in open conditions, respectively.
$Q_1$ and $Q_2$ are the power dissipations in Circuit-1 and Circuit-2 when the switches $S_1$ and $S_2$ are in closed conditions, respectively.

Which of the following statement(s) is(are) correct?

Two identical cells each of emf 1.5 V are connected in parallel across a parallel combination of two resistors each of resistance $20\ \Omega$. A voltmeter connected in the circuit measures 1.2 V. The internal resistance of each cell is :