Electromagnetism PYQ — Page 6

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 parallel plate air capacitor has a capacitance $C$. When it is half filled as show in figure with a dielectric constant $K = 5$, the percentage increase in the capacitance is _______. 

A $30$ cm long solenoid has $10$ turns per cm and area of $5$ cm$^2$. The current through the solenoid coil varies from $2$ A to $4$ A in $3.14$ s. The e.m.f. induced in the coil is $\alpha\times 10^{-5}$ V. The value $\alpha$ is ________.

The electric field of an electromagnetic wave travelling through a medium is given by $\vec{E}(x, t)=25 \sin \left(2.0 \times 10^{15} t-10^{7} x\right) \hat{n}$ then the refractive index of the medium is $\_\_\_\_$. (All given measurement are in SI units)

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 :

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

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 _______ $\Omega$.

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 $\_\_\_\_$ $\Omega$.

The electric current in the circuit is given as $i=i_{\mathrm{o}}(t / T)$. The r.m.s current for the period $t=0$ to $t=T$ is $\_\_\_\_$.

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 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 short bar magnet placed with its axis at $30^{\circ}$ with an external field of 800 Gauss, experiences a torque of $0.016 \mathrm{~N}. \mathrm{m}$. The work done in moving it from most stable to most unstable position is $\alpha \times 10^{-3} \mathrm{~J}$. The value of $\alpha$ is $\_\_\_\_$.

An insulated wire is wound so that it forms a flat coil with $N = 200$ turns. The radius of the innermost turn is $r_1 = 3$ cm, and of the outermost turn $r_2 = 6$ cm. If $20$ mA current flows in it then the magnetic moment will be $\alpha \times 10^{-2}$ A.m$^2$. The value of $\alpha$ is _____.

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)

Two resistors of $100 \Omega$ each are connected in series with a 9 V battery. A voltmeter of $400 \Omega$ resistance is connected to measure the voltage drop across one of the resistors. The voltmeter reading is $\_\_\_\_$ V.

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 battery with EMF $E$ and internal resistance $r$ is connected across a resistance $R$. The power consumption in $R$ will be maximum when :

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 figure given below shows an $LCR$ series circuit with two switches $S_1$ and $S_2$. When switch $S_1$ is closed keeping $S_2$ open, the phase difference $(\phi)$ between the current and source voltage is $30°$ and phase difference is $60°$ when $S_2$ is closed keeping $S_1$ open. The value of $(3L_1 - L_2)$ is _______ H. 

If an optical medium possesses a relative permeability of $\frac{10}{\pi}$ and relative permittivity of $\frac{1}{0.0885}$, then the velocity of light is greater in vacuum than that in this medium by ________ times. $\left(\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}, \epsilon_0=8.85 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right.$ $\left.\mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)$

Let $B_1$ be the magnitude of magnetic field at center of a circular coil of radius $R$ carrying current $I$. Let $B_2$ be the magnitude of magnetic field at an axial distance ' $x$ ' from the center. For $x: R=3: 4, \frac{B_2}{B_1}$ is :