Current Electricity

A cell E$_1$ of emf 6 V and internal resistance 2 Ω is connected with another cell E$_2$ of emf 4 V and internal resistance 8 Ω (as shown in the figure). The potential difference across points X and Y is :

A current through a wire depends on time as

$i=\alpha_0t+\beta t^2$

where $\alpha_0$ = 20 A/s and β = 8 A s$^{-2}$. Find the charge crossed through a section of the wire in 15 s.

Shown in the figure is a semicircular metallic strip that has thickness $t$ and resistivity $\rho$. Its inner radius is $R_1$ and outer radius is $R_2$. If a voltage $V_0$ is applied between its two ends, a current $I$ flows in it. In addition, it is observed that a transverse voltage $\Delta V$ develops between its inner and outer surfaces due to purely kinetic effects of moving electrons (ignore any role of the magnetic field due to the current). Then (figure is schematic and not drawn to scale)

In the balanced condition, the values of the resistances of the four arms of a Wheatstone bridge are shown in the figure below. The resistance $R_3$ has temperature coefficient $0.0004\ ^\circ\mathrm{C}^{-1}$. If the temperature of $R_3$ is increased by $100\ ^\circ$C, the voltage developed between $S$ and $T$ will be ______ volt.

In the circuit shown, initially there is no charge on capacitors and keys $S_1$ and $S_2$ are open. The values of the capacitors are $C_1 = 10\ \mu$F, $C_2 = 30\ \mu$F and $C_3 = C_4 = 80\ \mu$F.

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

Two identical moving coil galvanometers have 10 Ω resistance and full scale deflection at 2 μA current. One of them is converted into a voltmeter of 100 mV full scale reading and the other into an Ammeter of 1 mA full scale current using appropriate resistors. These are then used to measure the voltage and current in the Ohm's law experiment with $R = 1000$ Ω resistor by using an ideal cell. Which of the following statement(s) is/are correct?

In the figure below, the switches $S_1$ and $S_2$ are closed simultaneously at $t = 0$ and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current $I$ in the middle wire reaches its maximum magnitude $I_{max}$ at time $t = \tau$. Which of the following statements is (are) true?

A moving coil galvanometer has 50 turns and each turn has an area $2 \times 10^{-4}\ \mathrm{m^2}$. The magnetic field produced by the magnet inside the galvanometer is 0.02 T. The torsional constant of the suspension wire is $10^{-4}\ \mathrm{N\,m\,rad^{-1}}$. When a current flows through the galvanometer, a full scale deflection occurs if the coil rotates by 0.2 rad. The resistance of the coil of the galvanometer is 50 Ω. This galvanometer is to be converted into an ammeter capable of measuring current in the range 0 − 1.0 A. For this purpose, a shunt resistance is to be added in parallel to the galvanometer. The value of this shunt resistance, in ohms, is __________.

A source of constant voltage $V$ is connected to a resistance $R$ and two ideal inductors $L_1$ and $L_2$ through a switch $S$ as shown. There is no mutual inductance between the two inductors. The switch $S$ is initially open. At $t = 0$, the switch is closed and current begins to flow. Which of the following options is/are correct?

In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be :

In the above circuit the current in each resistance is :

When a current of 5 mA is passed through a galvanometer having a coil of resistance 15 Ω, it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range 0 − 10 V is :

Which of the following statements is false ?

A 9 V battery with internal resistance of 0.5 Ω is connected across an infinite network as shown in the figure. All ammeters $A_1$, $A_2$, $A_3$ and voltmeter V are ideal.

Choose correct statement.

A potentiometer PQ is set up to compare two resistances as shown in the figure. The ammeter A in the circuit reads 1.0 A when two way key $K_3$ is open. The balance point is at a length $l_1$ cm from P when two way key $K_3$ is plugged in between 2 and 1, while the balance point is at a length $l_2$ cm from P when key $K_3$ is plugged in between 3 and 1. The ratio of two resistances $\dfrac{R_1}{R_2}$, is found to be :

A uniform wire of length l and radius r has a resistance of 100 Ω. It is recast into a wire of radius $\dfrac r2$. The resistance of new wire will be :

The figure shows three circuits I, II and III which are connected to a 3V battery. If the powers dissipated by the configurations I, II and III are $P_1$, $P_2$ and $P_3$ respectively, then :

In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance P = 4 Ω and the neutral point N is at 60 cm from A. Now an unknown resistance R is connected in series to P and the new position of the neutral point is at 80 cm from A. The value of unknown resistance R is :

An infinite line charge of uniform electric charge density $\lambda$ lies along the axis of an electrically conducting infinite cylindrical shell of radius $R$. At time $t=0$, the space inside the cylinder is filled with a material of permittivity $\varepsilon$ and electrical conductivity $\sigma$. The electrical conduction in the material follows Ohm's law. Which one of the following graphs best describes the subsequent variation of the magnitude of current density $j(t)$ at any point in the material?

An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the following statement(s) is(are) true?