JEE Physics Test Series Quiz-7

A small bar magnet is moved through a coil at a constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer G attached across the coil?

Three positions shown describe (1) the magnet’s entry (2) the magnet is completely inside and (3) the magnet’s exit.

An elliptical loop having resistance \(R\), of semi-major axis \(a\), and semi-minor axis \(b\) is placed in a magnetic field as shown in the figure. If the loop is rotated about the \(x\)-axis with angular frequency \(\omega\), the average power loss in the loop due to Joule heating is :

A uniform magnetic field \(B\) exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of \(4 \mathrm{~mm}\) and a total length of \(30 \mathrm{~cm}\). The magnetic field changes with time at a steady rate \(d B / d t=0.032 \mathrm{Ts}^{-1}\). The induced current in the loop is close to (Resistivity of the metal wire is \(\left.1.23 \times 10^{-8} \Omega \mathrm{m}\right)\)

At time \(t=0\) magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next \(5 \mathrm{~s}\), then induced EMF in the loop is:

Consider a circular coil of wire carrying constant current \(I\), forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by \(\phi_i\). The magnetic flux through the area of the circular coil area is given by \(\phi_0\). Which of the following option is correct?

A long solenoid of radius \(R\) carries a time \((t)\) – dependent current \(I(t)=I_0 t(1-t)\). A ring of radius \(2 R\) is placed coaxially near its middle. During the time interval \(0 \leq t \leq 1\), the induced current \(\left(I_R\right)\) and the induced \(\operatorname{EMF}\left(V_R\right)\) in the ring change as:

A planar loop of wire rotates in a uniform magnetic field. Initially, at \(t=0\), the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of \(10 \mathrm{~s}\) about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at:

A very long solenoid of radius \(R\) is carrying current \(\mathrm{I}(\mathrm{t})=\mathrm{kte}^{-\mathrm{at}}(k>0)\), as a function of time \((t \geq 0)\). Counterclockwise current is taken to be positive. A circular conducting coil of radius \(2 \mathrm{R}\) is placed in the equatorial plane of the solenoid and concentric with the solenoid. The current induced in the outer coil is correctly depicted, as a function of time, by:

The self-induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from \(10 \mathrm{~A}\) to 25 \(A\) in 1s, the change in the energy of the inductance is:

A conducting circular loop made of a thin wire has area \(3.5 \times 10^{-3} \mathrm{~m}^2\) and resistance \(10 \Omega\). It is placed perpendicular to a time-dependent magnetic field \(\mathrm{B}(\mathrm{t})=(0.4 \mathrm{~T}) \sin (50 \pi \mathrm{t})\). The net charge flowing through the loop during \(t=0\) \(\mathrm{s}\) and \(\mathrm{t}=10 \mathrm{~ms}\) is close to:

In a coil of resistance \(100 \Omega\), a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is

A conducting metal circular-wire-loop of radius \(r\) is placed perpendicular to a magnetic field which varies with time as \(\mathrm{B}=\mathrm{B}_0 \mathrm{e}^{-t / \tau} \text {, where } \mathrm{B}_0 \text { and } \tau \text { are constants, at time } \mathrm{t}=0 \text {. }\) If the resistance of the loop is \(\mathrm{R}\) then the heat generated in the loop after a long time \((t \rightarrow \infty)\) is :

When current in a coil changes from \(5 \mathrm{~A}\) to \(2 \mathrm{~A}\) in \(0.1 \mathrm{~s}\), the average voltage of \(50 \mathrm{~V}\) is produced. The self-inductance of the coil is:

The figure shows a circular area of radius \(\mathrm{R}\) where a uniform magnetic field \(\vec{B}\) is going into the plane of the paper and increasing in magnitude at a constant rate.

In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field \(\mathrm{E}(\mathrm{r})\)?

A circular loop of radius \(0.3 \mathrm{~cm}\) lies parallel to a much bigger circular loop of radius \(20 \mathrm{~cm}\). The centre of the small loop is on the axis of the bigger loop. The distance between their centres is \(15 \mathrm{~cm}\). If a current of \(2.0 \mathrm{~A}\) flows through the smaller loop, then the flux linked with the bigger loop is

The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. \(I_1\) and \(I_2\) are the currents in the segments \(\mathbf{a b}\) and \(\mathbf{c d}\). Then,

A small bar magnet is being slowly inserted with constant velocity inside a solenoid as shown in the figure. Which graph best represents the relationship between emf induced with time

A thin circular ring of area \(A\) is held perpendicular to a uniform magnetic field of induction \(B\). \(A\) small cut is made in the ring and a galvanometer is connected across the ends such that the total resistance of the circuit is \(R\). When the ring is suddenly squeezed to zero area, the charge flowing through the galvanometer is

A series \(\mathrm{R}-\mathrm{C}\) combination is connected to an \(\mathrm{AC}\) voltage of angular frequency \(\omega=500 \mathrm{radian} / \mathrm{s}\). If the impedance of the R-C circuit is \(R \sqrt{1.25}\), the time constant (in milliseconds) of the circuit is

The figure shows a square loop \(L\) of side \(5 \mathrm{~cm}\) which is connected to a network of resistances. The whole setup is moving towards the right with a constant speed of \(1 \mathrm{~cm} \mathrm{~s}^{-1}\). At some instant, a part of \(\mathrm{L}\) is in a uniform magnetic field of \(1 \mathrm{~T}\), perpendicular to the plane of the loop. If the resistance of \(L\) is \(1.7 \Omega\), the current in the loop at that instant will be close to :

The total number of turns and cross-section area in a solenoid is fixed. However, its length \(L\) is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to:

A \(10 \mathrm{~m}\) long horizontal wire extends from North East to South West. It is falling with a speed of \(5.0 \mathrm{~ms}^{-1}\), at right angles to the horizontal component of the earth’s magnetic field, of \(0.3 \times 10^{-4} \mathrm{~Wb} / \mathrm{m}^2\). The value of the induced emf in wire is :

A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per unit length of the frame the same, then the self-inductance of the coil:

An insulating thin rod of length \(l\) has a linear charge density \(\rho(x)=\rho_0 \frac{x}{l}\) on it. The rod is rotated about an axis passing through the origin \((x=0)\) and perpendicular to the rod. If the rod makes \(\mathrm{n}\) rotations per second, then the time-averaged magnetic moment of the rod is:

A conducting square loop of side \(L\) and resistance \(R\) moves in its plane with a uniform velocity \(v\) perpendicular to one of its sides. A magnetic induction \(B\), constant in time and space, pointing perpendicular and into the plane of the loop exists everywhere. The current induced in the loop is:

An alternating voltage \(v(t)=220 \sin 100 \pi t\) volt is applied to a purely resistive load of \(50 \Omega\). The time taken for the current to rise from half of the peak value to the peak value is:

A sinusoidal voltage \(V(t)=100 \sin (500 t)\) is applied across a pure inductance of \(\mathrm{L}=0.02 \mathrm{H}\). The current through the coil is:

An AC circuit has \(R=100 \Omega, C=2 \mu \mathrm{F}\) and \(L=80 \mathrm{mH}\), connected in series. The quality factor of the circuit is :

A series \(L-R\) circuit is connected to a battery of emf \(V\). If the circuit is switched on at \(t=0\), then the time at which the energy stored in the inductor reaches \(\left(\frac{1}{n}\right)\) times of its maximum value, is:

A \(750 \mathrm{~Hz}, 20 \mathrm{~V}\) (rms) source is connected to a resistance of \(100 \Omega\), an inductance of \(0.1803 \mathrm{H}\) and a capacitance of 10\(\mu \mathrm{F}\) all in series. The time in which the resistance (heat capacity \(2 \mathrm{~J} /{ }^{\circ} \mathrm{C}\) ) will get heated by \(10^{\circ} \mathrm{C}\). (assume no loss of heat to the surroundings) is close to :

An inductance coil has a reactance of \(100 \Omega\). When an AC signal of frequency \(1000 \mathrm{~Hz}\) is applied to the coil, the applied voltage leads the current by \(45^{\circ}\). The self-inductance of the coil is :

Consider the LR circuit shown in the figure. If the switch \(\mathrm{S}\) is closed at \(\mathrm{t}=0\) then the amount of charge that passes through the battery between \(\mathrm{t}=0\) and \(t=\frac{L}{R}\) is :

A 20 Henry inductor coil is connected to a \(10 \mathrm{ohm}\) resistance in series as shown in the figure. The time at which the rate of dissipation of energy (Joule’s heat) across the resistance is equal to the rate at which magnetic energy is stored in the inductor is :

In the figure shown, a circuit contains two identical resistors with resistance \(R=5 \Omega\) and an inductance with \(\mathrm{L}\) \(=2 \mathrm{mH}\). An ideal battery of \(15 \mathrm{~V}\) is connected in the circuit. What will be the current through the battery long after the switch is closed?

In the below circuit, \(\mathrm{C}=\frac{\sqrt{3}}{2} \mu \mathrm{F}, \mathrm{R}_2=20 \Omega, \mathrm{L}=\frac{\sqrt{3}}{10} \mathrm{H}\) and \(R_1=10 \Omega \text {. Current in } L-R_1 \text { path is } I_1 \text { and in C- } R_2 \text { path it is }\) \(I_2\). The voltage of A.C source is given by, \(V=200 \sqrt{2} \sin (100 t) \text { volts. The phase difference between } I_1 \text { and } I_2 \text { is: }\)

In the circuit shown,

the switch \(\mathrm{S}_1\) is closed at time \(\mathrm{t}=0\) and the switch \(\mathrm{S}_2\) is kept open. At some later time \(\left(t_0\right)\), the switch \(S_1\) is opened and \(\mathrm{S}_2\) is closed. the behaviour of the current \(\mathrm{I}\) as a function of time ‘ \(t\) ‘ is given by:

In \(\mathrm{LC}\) circuit the inductance \(\mathrm{L}=40 \mathrm{mH}\) and capacitance \(\mathrm{C}\) \(=100.00 \mu \mathrm{F}\). If a voltage \(\mathrm{V}(t)=10 \sin (314 t)\) is applied to the circuit, the current in the circuit is given as:

As shown in the figure, a battery of emf \(\in\) is connected to an inductor \(L\) and resistance \(R\) in series. The switch is closed at \(t=0\). The total charge that flows from the battery, between \(t\) \(=0\) and \(t=t_c\left(t_c\right.\) is the time constant of the circuit \()\) is:

A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant ‘ \(b\) ‘, the correct equivalence would be:

An emf of \(20 \mathrm{~V}\) is applied at time \(t=0\) to a circuit containing in series \(10 \mathrm{mH}\) inductor and \(5 \Omega\) resistor. The ratio of the currents at time \(t=\infty\) and at \(t=40 \mathrm{~s}\) is close to: \(\text { (Take } \left.e^2=7.389\right)\)

In an a.c. circuit, the instantaneous e.m.f. and current are given by
\(
\begin{aligned}
& e=100 \sin 30 t \\
& i=20 \sin \left(30 \mathrm{t}-\frac{\pi}{4}\right)
\end{aligned}
\)
In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively.

For an RLC circuit driven with a voltage of amplitude \(v_{\mathrm{m}}\) and frequency \(\omega_0=\frac{1}{\sqrt{\mathrm{LC}}}\) the current exhibits resonance. The quality factor, \(\)Q\(\) is given by:

A sinusoidal voltage of peak value \(283 \mathrm{~V}\) and angular frequency \(320 / \mathrm{s}\) is applied to a series LCR circuit. Given that \(\mathrm{R}=5 \Omega, \mathrm{L}=25 \mathrm{mH}\) and \(\mathrm{C}=1000 \mu \mathrm{F}\). The total impedance, and phase difference between the voltage across the source and the current will respectively be :

An arc lamp requires a direct current of \(10 \mathrm{~A}\) at \(80 \mathrm{~V}\) to function. If it is connected to a \(220 \mathrm{~V}\) (rms), \(50 \mathrm{~Hz} \mathrm{~AC}\) supply, the series inductor needed for it to work is close to :

An inductor \((L=0.03 \mathrm{~H})\) and a resistor \((\mathrm{R}=0.15 \mathrm{k} \Omega)\) are connected in series to a battery of \(15 \mathrm{~V}\) emf in a circuit shown below. The key \(\mathrm{K}_1\) has been kept closed for a long time. Then at \(t=0, K_1\) is opened and key \(K_2\) is closed simultaneously. At \(\mathrm{t}=1 \mathrm{~ms}\), the current in the circuit will be: \(\left(e^5 \cong 150\right)\)

For the LCR circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor C’, when joined with the capacitor \(\mathrm{C}\) present in the circuit, makes the power factor of the circuit unity. The capacitor \(\mathrm{C}^{\prime}\), must have been connected in :

In the circuit shown here, the point ‘ \(\mathrm{C}\) ‘ is kept connected to point ‘ \(\mathrm{A}\) ‘ till the current flowing through the circuit becomes constant. Afterward, suddenly, point ‘ \(C\) ‘ is disconnected from point ‘ \(A\) ‘ and connected to point ‘ \(B\) ‘ at time \(t=0\). Ratio of the voltage across resistance and the inductor at \(t=L / R\) will be equal to:

When the rms voltages \(V_L, V_C\) and \(V_R\) are measured respectively across the inductor \(\mathrm{L}\), the capacitor \(\mathrm{C}\) and the resistor \(\mathrm{R}\) in a series \(\mathrm{LCR}\) circuit connected to an \(\mathrm{AC}\) source, it is found that the ratio \(V_L: V_C: V_R=1: 2: 3\). If the rms voltage of the \(A C\) sources is \(100 \mathrm{~V}\), the \(V_R\) is close to:

A series LR circuit is connected to an ac source of frequency \(\omega\) and the inductive reactance is equal to \(2 R[latex]. A capacitance of capacitive reactance equal to [latex]R\) is added in series with \(L\) and \(R\). The ratio of the new power factor to the old one is :

An \(\mathrm{AC}\) voltage source of variable angular frequency \(\omega\) and fixed amplitude \(V_0\) is connected in series with a capacitance \(C\) and an electric bulb of resistance \(R\) (inductance zero). When \(\omega\) is increased