Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in the following: If $y=\cos ^{-1}\left(4 x^{3}-3 x\right)$ then $\frac{d y}{d x}=$ ? A. $\frac{3}{\sqrt{1-x^{2}}}$ B. $\frac{-3}{\sqrt{1-\mathrm{x}^{2}}}$ C. $\frac{4}{\sqrt{1-x^{2}}}$ D. $\frac{4}{\left(3 x^{2}-1\right)}$ Solution: $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{-3}{\sqrt{1-\mathrm{x}^{2}}}$...
Read More →The sunlight reaching the earth has maximum electric field of
Question: The sunlight reaching the earth has maximum electric field of $810 \mathrm{~V} / \mathrm{m}$. What is the maximum magnetic field in this light? Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=\sin ^{-1}\left(3 x-4 x^{3}\right)$ then $\frac{d y}{d x}=?$ A. $\frac{3}{\sqrt{1-x^{2}}}$ B. $\frac{-4}{\sqrt{1-x^{2}}}$ C. $\frac{3}{\sqrt{1+\mathrm{x}^{2}}}$ D. none of these Solution:...
Read More →The value of
Question: Using $B=\mu_{0} H_{\text {find the ratio }} E_{0} / H_{0}$ for a plane electromagnetic wave propagating through vacuum. Show that it has the dimension of electric resistance. This ratio is a universal constant called the impedance of free space. Solution:...
Read More →Consider the situation of the previous problem.
Question: Consider the situation of the previous problem. Define displacement resistance $R_{d}=V / i_{d}$ of the space between the plates where $\mathrm{V}$ is the potential difference between the plates and $\mathrm{i}_{\mathrm{d}}$ is the displacement current. Show that $\mathrm{R}_{\mathrm{d}}$ varies with time as $R_{d}=R\left(e^{1 / r}-1\right)$. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)})$ against the correct answer in the following: If $y=\tan ^{-1}\left(\frac{a \cos x-b \sin x}{b \cos x+a \sin x}\right)$ then $\frac{d y}{d x}=?$ A. $\frac{a}{b}$ B. $\frac{-b}{a}$ C. 1 D. $-1$ Solution:...
Read More →A parallel-plate capacitor having plate-area A
Question: A parallel-plate capacitor having plate-area $\mathrm{A}$ and plate separation $\mathrm{d}$ is joined to a battery of emf $\epsilon$ and internal resistance $\mathrm{R}$ at $\mathrm{t}=0$. Consider a plane surface of area $\mathrm{A} / 2$, parallel to the plates and situated symmetrically between them. Find the displacement current through this surface as a function of time. Solution:...
Read More →A point charge is moving along a straight line with a constant velocity v.
Question: A point charge is moving along a straight line with a constant velocity v. Consider a small area A perpendicular to the direction of motion of the charge. Calculate the displacement current through the area when its distance from the charge is $x$. The value of $x$ is not large so that the electric field at any instant is essentially given by Coulomb's law. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=\tan ^{-1} \sqrt{\frac{1-\cos x}{1+\cos x}}$ then $\frac{d y}{d x}=$ A. $\frac{1}{2}$ B. $\frac{-1}{2}$ C. $\frac{1}{\left(1+x^{2}\right)}$ D. none of these Solution:...
Read More →Show that the direction of the displacement current
Question: Show that the direction of the displacement current $\varepsilon_{0}$ $\varepsilon_{0} \frac{d \varphi_{E}}{d t}$ are that of an electric current. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in the following: If $y=\tan ^{-1}\left\{\frac{\cos x}{1+\sin x}\right\}$ then $\frac{d y}{d x}=$ ? A. $\frac{1}{2}$ B. $\frac{-1}{2}$ C. 1 D. -1 Solution: $\frac{\mathrm{dy}}{\mathrm{dx}}=-\frac{1}{2}$...
Read More →A transformer has 50 turns in the primary and 100 in the secondary.
Question: A transformer has 50 turns in the primary and 100 in the secondary. If the primary is connected to $220 \mathrm{~V}$ DC supply, what will be the voltage across the secondary? Solution: Zero voltage across secondary coil as there is no change in flux....
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in the following: If $y=\tan ^{-1}\left\{\frac{\cos x+\sin x}{\cos x-\sin x}\right\}$ then $\frac{d y}{d x}=$ ? A. 1 B. $-1$ C. $\frac{1}{2}$ D. $\frac{-1}{2}$ Solution:...
Read More →Figure shows a typical circuit for low pass filter.
Question: Figure shows a typical circuit for low pass filter. An AC input $\mathrm{v}_{\mathrm{i}}=10 \mathrm{mV}$ is applied at the left end and the output $\mathrm{v}_{0}$ is received at the right end. Find the output voltages for $\mathrm{v}=10 \mathrm{kHz}, 100 \mathrm{kHz}, 1.0 \mathrm{MHz}$ and $10.0 \mathrm{MHz}$. Note that as the frequency is increased the output decreases and hence the name low pass filter. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=\tan ^{-1}\left(\frac{1-\cos x}{\sin x}\right)$ then $\frac{d y}{d x}=?$ A. 1 B. $-1$ C. $\frac{1}{2}$ D. $\frac{-1}{2}$ Solution: Given that $y=\tan ^{-1}\left(\frac{1-\cos x}{\sin x}\right)$...
Read More →An inductor-coil, a capacitor and an AC source of rms voltage 24V
Question: An inductor-coil, a capacitor and an AC source of rms voltage $24 \mathrm{~V}$ are connected in series. When the frequency of the source is varied, a maximum rms current of $6.0 \mathrm{~A}$ is observed. If this inductor coil is connected to a battery of emf $12 \mathrm{~V}$ and the internal resistance $4.0 \Omega$, what will be the current? Solution:...
Read More →An inductance of 2.0H,
Question: An inductance of $2.0 \mathrm{H}$, a capacitance of $18 \mu \mathrm{F}$ and a resistance of $10 \mathrm{k} \Omega$ are connected to an Ac source of $20 \mathrm{~V}$ with adjustable frequency. (a) What frequency should be chosen to maximize the current in the circuit? (b) What is the value of this maximum current? Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in the following: If $y=\sqrt{\frac{1+\tan x}{1-\tan x}}$ then $\frac{d y}{d x}=$ ? A. $\frac{1}{2} \sec ^{2} x \cdot \tan \left(x+\frac{\pi}{4}\right)$ B. $\frac{\sec ^{2}\left(x+\frac{\pi}{4}\right)}{2 \sqrt{\tan \left(x+\frac{\pi}{4}\right)}}$ C. $\frac{\sec ^{2}\left(\frac{x}{4}\right)}{\sqrt{\tan \left(x+\frac{\pi}{4}\right)}}$ D. none of these Solution:...
Read More →Consider the situation of the previous problem.
Question: Consider the situation of the previous problem. Find the average electric field energy stored in the capacitor and the average magnetic field energy stored in the coil. Solution:...
Read More →In a series LCR circuit with an AC source,
Question: In a series LCR circuit with an $\mathrm{AC}$ source, $\mathrm{R}=300 \Omega, \mathrm{C}=20 \mu \mathrm{F}, \mathrm{L}=1.0$ henry, $\varepsilon_{\mathrm{rms}}=50 \mathrm{~V}$ and $\mathrm{v}=50 / \pi \mathrm{Hz}$. Find (a) the rms current in the circuit. (b) The rms potential differences across the capacitor, the resistor and the inductor. Note that the sum of the rms potential differences across the three elements is greater than the rms voltage of the source. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=\sqrt{\frac{\sec x-1}{\sec x+1}}$ then $\frac{d y}{d x}=?$ A. $\sec ^{2} \mathrm{x}$ B. $\frac{1}{2} \sec ^{2} \frac{\mathrm{x}}{2}$ C. $\frac{-1}{2} \operatorname{cosec}^{2} \frac{\mathrm{x}}{2}$ D. none of these Solution:...
Read More →An electric bulb is designed to consume 55W
Question: An electric bulb is designed to consume $55 \mathrm{~W}$ when operated at 110 volts. It is connected to a $220 \mathrm{~V}$, $50 \mathrm{~Hz}$ line through a choke coil in series. What should be the coil for which the bulb gets correct voltage? Solution:...
Read More →In a series RC circuit with an AC source, R=300Ω,
Question: In a series $\mathrm{RC}$ circuit with an $\mathrm{AC}$ source, $\mathrm{R}=300 \Omega, \mathrm{C}=25 \mu \mathrm{F}, \varepsilon_{0}=50 \mathrm{v}$ and $\mathrm{v}=50 / \pi \mathrm{Hz}$. Find the peak current and the average power dissipated in the circuit. Solution:...
Read More →A resistor of resistance 100Ω is connected to an AC
Question: A resistor of resistance $100 \Omega$ is connected to an $\mathrm{AC}$ source $^{\varepsilon}=(12 \mathrm{~V}) \sin \left(250 \pi \mathrm{s}^{-1}\right) \mathrm{t}$. Find the energy dissipated as heat during $\mathrm{t}=0$ to $\mathrm{t}=0.1 \mathrm{~ms}$. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=\sqrt{\frac{1+\sin x}{1-\sin x}}$ then $\frac{d y}{d x}=?$ A. $\frac{1}{2} \sec ^{2}\left(\frac{\pi}{4}-\frac{\pi}{2}\right)$ B. $\frac{1}{2} \operatorname{cosec}^{2}\left(\frac{\pi}{4}-\frac{\pi}{2}\right)$ C. $\frac{1}{2} \operatorname{cosec}^{2}\left(\frac{\pi}{4}-\frac{\pi}{2}\right) \cot \left(\frac{\pi}{4}-\frac{\pi}{2}\right)$ D. none of these Solution:...
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