Ohm's Law in Vector Form

Q.

Why does inductance increase with the iron core?

Q. A wire of resistance $\text{R}$ is bent to form a square $\text{ABCD}$ as shown in the figure. The effective resistance between $\text{E}$ and $\text{C}$ is
($\text{E}$ is mid-point of arm $\text{CD}$)

1. $\frac{3}{4}\text{R}$
2. $\frac{1}{16}\text{R}$
3. $\frac{7}{64}\text{R}$
4. $\text{R}$

Q. If $\overrightarrow{E}=\hat{i}+\sqrt{2}\hat{j}+\sqrt{3}\hat{k}$, then find the Electric flux through surface of area $100{\text{m}}^2$ lying in the $\text{xy-plane}$ (in $\text{Vm}$)

1. $100$
2. $141.4$
3. $173.2$
4. $200$

Q. Variation of current passing through a conductor as the voltage applied across its ends is varied is shown in the diagram. If the resistance R is determined at points A, B, C and D, we will find that

1. $R_A=R_B$
2. $R_D>R_A$
3. $R_B>R_A$
4. None of these

Q. Two long straight parallel wires carries currents of $200\text{mA}$ and $1\text{A}$ in opposite directions. If the wires are $20\text{cm}$ apart, the distance of the neutral point from the $1\text{A}$ wire is- (in $\text{cm}$)

1. $25$
2. $35$
3. $40$
4. $55$

Q.

In a current-carrying conductor varying electric field generates

Q. The magnitude of electric field inside a conductor at any cross section is equal to the magnitude of current density.

1. False
2. True

Q. Assertion : Kirchhoff’s current law is valid at each plate of a capacitor carrying displacement current.

Reason : Magnitude of conduction current is equal to the magnitude of the displacement current.

1. Both assertion and reason are true, and reason is the correct explanation of assertion.
2. Both assertion and reason are true, but reason is not a correct explanation of assertion.
3. Assertion is true, but reason is false.
4. Assertion is false, but reason is true.

Q. In the figure ammeter reads $I_1$ and voltmeter reads $V_1$. Similarly in figure 2, ammeter reads $I_2$ and voltmeter reads $V_2$. Then which of the statements are true?

1. $V_1>V_2$ and $I_1>I_2$
2. $V_1>V_2$and $I_1<I_2$
3. $V_1>I_1$and $V_2>I_2$
4. $V_1=V_2$

Q. Which of the following is NOT a property of displacement current?

1. Displacement current exists in a space, where there is a varying electric field.
2. Displacement current does not exist under steady state conditions.
3. Displacement current obeys Ohm's law.
4. Displacement current is not a conventional electric current.

Q. If $V_D=12$ volt & $V_E=8$ volt then

1. $V_A=56volt$
2. $V_C=52volt$
3. $V_B=48volt$
4. $V_B=68volt$

Q. Answer the following question:

Q. Assertion :A current continues to flow in superconducting coil even after switch is off. Reason: Superconducting coils show Meissner effect.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. The electric field vector at any cross-section of a conductor and the current density vector both have the same direction

1. True
2. False

Q. In the circuits as shown in the figure, $S_1$ and $S_2$ are switches. $S_2$ remains closed for a long time and $S_1$ is opened. Now $S_1$ is also closed. Just after $S_1$ is closed, find the potential difference ($V$) across $R$ and $\frac{di}{dt}$ in $L$.

1. $\frac{\epsilon }{3},\frac{\epsilon }{3L}$
2. $\frac{\epsilon }{3},\frac{2\epsilon }{3L}$
3. $\frac{2\epsilon }{3},\frac{\epsilon }{3L}$
4. $\frac{2\epsilon }{3},\frac{2\epsilon }{3L}$

Q. In the following circuit diagram (fig) if the ammeter reading is zero, then the voltmeter reading will be

1. zero
2. $E_1+E_2$
3. $E_1$
4. $E_2$

Q. Energy density (in vacuum) at a place where electric field intensity $E$ is:

1. $\frac{1}{2}{\epsilon }_0{E}^2$
2. $\frac{1}{2}{\epsilon }_{0}E$
3. $\frac{E^2}{2{\epsilon }_0}$
4. $\frac{1}{2}E{\epsilon }_0^2$

Q. The electric field vector at any cross-section of a conductor and the current density vector both have the same direction

1. True
2. False

Q. A cylindrical wire of radius $0.5\text{mm}$ and conductivity $5\times {10}^7\text{S/m}$ is subjected to an electric field of $10\text{mV/m}$. The expected value of current in the wire will be $x^3\pi \text{mA}$. The value of $x$ is

Q. The magnitude of electric field inside a conductor at any cross section is equal to the magnitude of current density.

1. False
2. True

Q. what will be the effect on the position of zero deflection in a potentiometer if 1. length of potentiometer wire is doubled and 2. the current flowing in potentiometer wire is decreased ?

Q. state and explain with diagram maxwells modification of amperecircuital law

Q. Find the current in $AB$ at time $t$. What is its limiting value as $t\to \infty$?

Q. The magnitude of electric field inside a conductor at any cross section is equal to the magnitude of current density.

1. True
2. False

Q. For the circuit shown in figure, the impedance of the circuit will be

1. $50\Omega$
2. $90\Omega$
3. $60\Omega$
4. $120\Omega$

Q. If $V_D=12$ volt & $V_E=8$ volt then

1. $V_A=56volt$
2. $V_B=68volt$
3. $V_C=52volt$
4. $V_B=48volt$

Q. If $V_D=12\text{V}$ and $V_E=8\text{V}$ then

1. $V_A=56volt$
2. $V_B=68volt$
3. $V_C=52volt$
4. $V_B=48volt$

Q. If a Bismuth rod is introduced in the air coil as shown then current in the coil

1. increases
2. remains unchanged
3. decrreases
4. none of these

Q.

the conducting plate is charged to a potential of 4, 000volt. a second metal plate , charged to a potential of 1, 000 volt is brought near the first plate at a distance of 10cm. what is the field intensity at any point between the plates?

Q. If $\overrightarrow{E}=\hat{i}+\sqrt{2}\hat{j}+\sqrt{3}\hat{k}$, then find the Electric flux through surface of area $100{\text{m}}^2$ lying in the $\text{xy-plane}$ (in $\text{Vm}$)

1. $200$
2. $173.2$
3. $141.4$
4. $100$