EMI & Alternating Currents

Figure shows a coil C connected to a galvanometer G. When the North-pole of a bar magnet is pushed towards the coil, the pointer in the galvanometer deflects. Regarding this set up, the following statements are given:

Choose the correct answer from the options given below:

Figure shows a rectangular conductor PQRS in which the conductor rod PQ of length $l$ is free to move. The conductor PQ is moved towards the left with a constant velocity $v$ as shown. Assume that there is no loss of energy due to friction. What will be the magnetic flux linked with the loop PQRS (at an instantaneous position where length of loop is $x$) and the motional emf?

The average emf induced in a coil is $2\,\text{V}$ when current is changed in $0.4\,\text{s}$: (A) from $5\,\text{A}$ to $2\,\text{A}$ and the self-inductance of the coil is $0.266\,\text{mH}$ (B) from $4\,\text{A}$ to $4\,\text{A}$ in the opposite direction, the self-inductance of the coil is $0.10\,\text{mH}$ Choose the correct statement from the options given below:

An inductor of $500\,\text{mH}$ is in series with a resistance and a variable capacitor connected to a source of frequency $0.4\,\text{kHz}$. The value of capacitance of the capacitor to get a maximum current will be:

A $12\,\text{V}$ battery connected to a $6\,\Omega$, $10\,\text{mH}$ coil through a switch drives a constant current in the circuit. The switch is suddenly opened. Assuming that it took $1\,\text{ms}$ to open the switch, the average emf induced across the coil would be:

For an ac source rated at $220\,\text{V}$, $50\,\text{Hz}$, which of the following statements is correct?

Which of the following statements is not correct for electromagnetic induction?

In an ac circuit, the current leads the voltage by $\pi/2$. The circuit is __________________.

In a pair of adjacent coils, for a change of current in one of the coils from $0\,\text{A}$ to $10\,\text{A}$ in $0.25\,\text{s}$, the magnetic flux in the adjacent coil changes by $15\,\text{Wb}$. The mutual inductance of the coils is _____________.

A wire of irregular shape in figure (a) and a circular loop of wire in figure (b) are placed in different uniform magnetic fields. In figure (a), the magnetic field is perpendicular into the plane. In figure (b), the magnetic field is perpendicular out of the plane. The wire in figure (a) is turning into a circular loop and that in figure (b) into a narrow straight wire. The direction of induced current will be ________________.

Match List-I (graphs showing variation of opposition to flow of ac versus frequency) with circuit characteristic in List-II:

Choose the correct answer from the options given below:

A conducting ring of radius $r$ is placed in a varying magnetic field perpendicular to the plane of the ring. If the rate at which the magnetic field varies is $x$, the electric field intensity at any point of the ring is ___________.

A $50\,\text{Hz}$ ac current of crest value $1\,\text{A}$ flows through the primary of a transformer. If the mutual inductance between the primary and secondary be $0.5\,\text{H}$, the crest voltage induced in the secondary is ____________.

A long solenoid of diameter $0.1\,\text{m}$ has $2 \times 10^4\,\text{turns/m}$. At the centre of the solenoid a coil of $100\,\text{turns}$ and radius $0.01\,\text{m}$ is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to $0\,\text{A}$ from $4\,\text{A}$ in $0.05\,\text{s}$. If the resistance of the coil is $10\pi^2\,\Omega$, then the total charge flowing through the coil during this time is ___________.

Which one out of the following is NOT an application of eddy currents?

In an a.c. circuit, the rms voltage is $100\sqrt{2}\,\text{V}$. The peak value of voltage would be:

A square loop of copper wire is pulled through a region of uniform magnetic field as shown. Rank the pulling forces $F_A, F_B, F_C$ and $F_D$ that must be applied to keep the loop moving with constant speed ($\vec{v}$):

Find the effective impedance in the circuit if the source is (a) DC source and (b) High frequency AC source:

In AC circuits, the relation that holds is $Z = \frac{V}{I}$, where:

Choose the correct answer from the options given below:

When $100\,\text{V}$ dc is applied across a solenoid, a current of $1.0\,\text{A}$ flows in it. When $100\,\text{V}$ ac is applied across the same solenoid, the current drops to $0.5\,\text{A}$. If the frequency of the ac source is $50\,\text{Hz}$, the impedance and inductance of the solenoid are:

A circuit element 'X' when connected to peak voltage of 200 V, a peak current of 5 A flows which lags behind the voltage by $\frac{\pi}{2}$. A circuit element Y when connected to same peak voltage, same peak current flows which is in phase with the voltage. Now X and Y are connected in series with the same peak voltage. The rms value of current through the circuit will be :

Case based

Figure shows a metal rod PQ resting on the rails AB and positioned between the poles of a permanent magnet. The rails, the rod and the magnetic field are in three mutually perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod $= 15\,\text{cm}$, $B = 0.50\,\text{T}$, resistance of the closed loop containing the rod $= 180.0\,\text{m}\Omega$. Assume the field to be uniform.

Suppose K is open and the rod is moved with a speed of $12\,\text{cm/s}$ in the direction shown. The magnitude of the induced emf will be :

Case based

Figure shows a metal rod PQ resting on the rails AB and positioned between the poles of a permanent magnet. The rails, the rod and the magnetic field are in three mutually perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod $= 15\,\text{cm}$, $B = 0.50\,\text{T}$, resistance of the closed loop containing the rod $= 180.0\,\text{m}\Omega$. Assume the field to be uniform.

The magnetic force experienced by the rod when K is closed will be :

Case based

Figure shows a metal rod PQ resting on the rails AB and positioned between the poles of a permanent magnet. The rails, the rod and the magnetic field are in three mutually perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod $= 15\,\text{cm}$, $B = 0.50\,\text{T}$, resistance of the closed loop containing the rod $= 180.0\,\text{m}\Omega$. Assume the field to be uniform.

The power required (by an external agent) to keep the rod moving at the same speed ($= 12\,\text{cm/s}$) when K is closed will be :

Case based

Figure shows a metal rod PQ resting on the rails AB and positioned between the poles of a permanent magnet. The rails, the rod and the magnetic field are in three mutually perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod $= 15\,\text{cm}$, $B = 0.50\,\text{T}$, resistance of the closed loop containing the rod $= 180.0\,\text{m}\Omega$. Assume the field to be uniform.

The power dissipated as heat in the closed circuit is :

Case based

Figure shows a metal rod PQ resting on the rails AB and positioned between the poles of a permanent magnet. The rails, the rod and the magnetic field are in three mutually perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod $= 15\,\text{cm}$, $B = 0.50\,\text{T}$, resistance of the closed loop containing the rod $= 180.0\,\text{m}\Omega$. Assume the field to be uniform.

The induced emf produced in the moving rod if the magnetic field becomes parallel to the rails instead of being perpendicular will be :