Electromagnetism PYQ — Page 5

Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :

There are three co-centric conducting spherical shells $A, B$ and $C$ of radii $a, b$ and $c$ respectively $(c>b>a)$ and they are charged with charge $q_{1}, q_{2}$ and $q_{3}$ respectively. The potentials of the spheres $A, B$ and $C$ respectively, are :

In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as $10\text{ V}$ and $5\text{ A}$, respectively. The least counts of voltmeter and ammeter are $500\text{ mV}$ and $200\text{ mA}$, respectively. The estimated error in the resistance measurement is _______ $\Omega$.

From the circuit given below, the capacitance between terminals $A$ and $B$ shown in the circuit is ______ $\mu$F. (take $C_1=C_2=C_3=1$ $\mu$F and $C_4=2$ $\mu$F.) 

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop is $\_\_\_\_$ mV.

For the two cells having same EMF $E$ and internal resistance $r$, the current passing through the external resistor $6 \Omega$ is same when both the cells are connected either in parallel or in series. The value of internal resistance $r$ is $\_\_\_\_$ $\Omega$.

Two cells of emfs $1$ V and $2$ V and internal resistance $2\,\Omega$ and $1\,\Omega$, 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 $\dfrac{\alpha}{5}$ A. The value of $\alpha$ is __________.

A point light source emits E.M. waves in free space. A detector, placed at a distance of $L$ m, measures the intensity as $I_o$. The detector is now shifted to another location on the same spherical surface ensuring the angle between original location and new location as $45°$. The measured intensity at new location will be _______.

A series LCR circuit with $R = 20\ \Omega$, $L = 1.6\text{ H}$ and $C = 40\ \mu\text{F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is _______ $\Omega$.

A circular loop of radius $20\text{ cm}$ and resistance $2\ \Omega$ is placed in a time varying magnetic field $\vec{B} = (2t^2 + 2t + 3)\text{ T}$. At $t = 0$, for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at $t = 3\text{ s}$ is $\dfrac{\alpha}{50}\text{ A}$. The value of $\alpha$ is _______. (Take $\pi = 22/7$)

A long cylindrical conductor with large cross section carries an electric current distributed uniformly over its cross-section. Magnetic field due to this current is : A. maximum at either ends of the conductor and minimum at the midpoint B. maximum at the axis of the conductor C. minimum at the surface of the conductor D. minimum at the axis of the conductor E. same at all points in the cross-section of the conductor Choose the correct answer from the options given below :

A regular hexagon is formed by six wires each of resistance $r \Omega$ and the corners are joined to the centre by wires of same resistance. If the current enters at one corner and leaves at the opposite corner, the equivalent resistance of the hexagon between the two opposite corners will be

A parallel plate capacitor is having separation between plates $0.885$ mm. It has a capacitance of $1\,\mu$F when the space between the plates is filled with an insulating material of resistivity $1\times 10^{13}\,\Omega$m and resistance $17.7\times 10^{14}\,\Omega$. Relative permittivity of the insulating material is $\alpha\times 10^7$. The value of $\alpha$ is ________. (Take permittivity of free space $=8.85\times 10^{-12}$ F/m)

The space between the plates of a parallel plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants $K_{1}=2, K_{2}=3$ and $K_{3}=5$ (as shown in figure). If new capacitance is $\frac{n}{3} C$ then the value of $n$ is $\_\_\_\_$. 

A current carrying circular loop of radius $2$ cm with unit normal $\hat{n} = \dfrac{\hat{k}+\hat{i}}{\sqrt{2}}$ is placed in a magnetic field, $\vec{B} = B_0(3\hat{i}+2\hat{k})$. If $B_0 = 4\times 10^{-3}$ T and current $I=100\sqrt{2}$ A, the torque experienced by the loop is ________ Wb·A. ($\pi=3.14$)

A cylindrical conductor of length 2 m and area of cross-section $0.2 \mathrm{~mm}^{2}$ carries an electric current of 1.6 A when its ends are connected to a 2 V battery. Mobility of electrons in the conductor is $\alpha \times 10^{-3} \mathrm{~m}^{2} / V. s$. The value of $\alpha$ is : (electron concentration $=5 \times 10^{28} / \mathrm{m}^{3}$ and electron charge $\left.=1.6 \times 10^{-19} \mathrm{C}\right)$

A LCR series circuit driven with $E_{rms} = 90$ V at frequency $f_d = 30$ Hz has resistance $R = 80\,\Omega$, an inductance with inductive reactance $X_L = 20.0\,\Omega$ and capacitance with capacitive reactance $X_C = 80.0\,\Omega$. The power factor of the circuit is _______.

The electric field in a plane electromagnetic wave is given by : $E_{y}=69 \sin \left[0.6 \times 10^{3} x-1.8 \times 10^{11} t\right] \mathrm{V} / \mathrm{m}$. The expression for magnetic field associated with this electromagnetic wave is $\_\_\_\_$ T.

In the given circuit below inductance values of $L_1$, $L_2$ and $L_3$ are same. The magnetic energy stored in the entire circuit is $(U_t)$ and that stored in the $L_2$ inductor is $(U_l)$. $U_t / U_l$ is __________. (Ignore the mutual inductance if any) 

The charged particle moving in a uniform magnetic field of $(3\hat{i} + 2\hat{j})$ T has an acceleration $\left(4\hat{i} - \dfrac{x}{2}\hat{j}\right)$ m/s$^2$. The value of $x$ is __________.

Identify the correct statements : A. Electrostatic field lines form closed loops. B. The electric field lines point radially outward when charge is greater than zero. C. The Gauss - Law is valid only for inverse - square force. D. The workdone in moving a charged particle in a static electric field around a closed path is zero. E. The motion of a particle under Coulomb's force must take place in a plane. Choose the correct answer from the options given below :

A point charge $q=1 \mu \mathrm{C}$ is located at a distance 2 cm from one end of a thin insulating wire of length 10 cm having a charge $Q=24 \mu \mathrm{C}$, distributed uniformly along its length, as shown in figure. Force between $q$ and wire is $\_\_\_\_$ N. (Use : $\frac{1}{4 \pi \epsilon_{\mathrm{o}}}=9 \times 10^{9} \mathrm{~N}. \mathrm{m}^{2} / \mathrm{C}^{2}$) 

Consider a circuit consisting of a capacitor ($20\ \mu$F), resistor ($100\ \Omega$) and two identical diodes as shown in figure. The resistance of diode under forward biasing condition is $10\ \Omega$. The time constant of the circuit is $\alpha \times 10^{-3}$ s. The value of $\alpha$ is _____ 

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