A plane electromagnetic wave propagating
Question: A plane electromagnetic wave propagating along x-direction can have the following pairs of E and B (a) Ex, By (b) Ey, Bz (c) Bx, Ey (d) Ez, By Solution: (b) Ey, Bz (d) Ez, By...
Read More →An electromagnetic wave travelling along
Question: An electromagnetic wave travelling along the z-axis is given as: E = E0cos (kz ꞷt). Choose the correct options from the following (a) the associated magnetic field is given as $B=\frac{1}{c} \hat{k} \times E=\frac{1}{\omega}(\hat{k} \times E)$ (b) the electromagnetic field can be written in terms of the associated magnetic field as $E=c(B \times \hat{k})$ (c) $\hat{k} \cdot E=0, \hat{k} \cdot B=0$ (d) $\hat{k} \times E=0, \hat{k} \times B=0$ Solution: (a) the associated magnetic field ...
Read More →Evaluate the integral:
Question: Evaluate the integral: $\int \frac{2 x-3}{x^{2}+6 x+13} d x$ Solution: $I=\int \frac{2 x-3}{x^{2}+6 x+13} d x$ As we can see that there is a term of $x$ in numerator and derivative of $x^{2}$ is also $2 x$. So there is a chance that we can make a substitution for $x^{2}+6 x+13$ and I can be reduced to a fundamental integration. As $\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{x}^{2}+6 \mathrm{x}+13\right)=2 \mathrm{x}+6$ $\therefore$ Let, $2 x-3=A(2 x+6)+B$ $\Rightarrow 2 x-3=2 A x+6 A+...
Read More →An electromagnetic wave travels
Question: An electromagnetic wave travels in vacuum along z-direction: $E=\left(E_{1} \hat{i}+E_{2} \hat{j}\right) \cos (k z-\omega t)$. Choose the correct options from the following: (a) the associated magnetic field is given as $B=\frac{1}{c}\left(E_{1} \hat{i}-E_{2} \hat{j}\right) \cos (k z-\omega t)$ (c) the given electromagnetic field is circularly polarised (d) the given electromagnetic waves is plane polarised Solution: (a) the associated magnetic field is given as $B=\frac{1}{c}\left(E_{...
Read More →Find the mean deviation about the mean for the following data :
Question: Find the mean deviation about the mean for the following data : Solution: we make the following table form the given data Therefore, $\overline{\mathrm{X}}=\frac{\sum_{\mathrm{i}=1}^{7} \mathrm{f}_{\mathrm{i}} x_{\mathrm{i}}}{\sum_{\mathrm{i}=1}^{7} \mathrm{f}_{\mathrm{i}}}=\frac{3100}{50}=62$...
Read More →An EM wave radiates outwards from a dipole antenna,
Question: An EM wave radiates outwards from a dipole antenna, with E0 as the amplitude of its electric field vector. The electric field E0 which transports significant energy from the source falls off as (a) 1/r3 (b) 1/r2 (c) 1/r (d) remains constant Solution: (c) 1/r...
Read More →The ratio of contributions made by the electric
Question: The ratio of contributions made by the electric field and magnetic field components to the intensity of an EM wave is (a) c: 1 (b) c2: 1 (c) 1: 1 (d) c: 1 Solution: (c) 1: 1...
Read More →If E and B represent electric and magnetic field
Question: If E and B represent electric and magnetic field vectors of the electromagnetic wave, the direction of propagation of the electromagnetic wave is along (a) E (b) B (c) B E (d) E B Solution: (d) E B...
Read More →Find the mean deviation about the mean for the following data :
Question: Find the mean deviation about the mean for the following data : Solution: Therefore, $\overline{\mathrm{X}}=\frac{\sum_{\mathrm{i}=1}^{7} \mathrm{f}_{\mathrm{i}} x_{\mathrm{i}}}{\sum_{\mathrm{i}=1}^{7} \mathrm{f}_{\mathrm{i}}}=\frac{3100}{50}=62$...
Read More →The electric field intensity produced by the radiations
Question: The electric field intensity produced by the radiations coming from 100 W bulb at a 3 m distance is E. The electric field intensity produced by the radiations coming from 50 W bulb at the same distance is (a) E/2 (b) 2E (c) E/2 (d) 2E Solution: (c) E/2...
Read More →Light with an energy flux of 20 W/cm2 falls on a non-reflecting
Question: Light with an energy flux of 20 W/cm2 falls on a non-reflecting surface at normal incidence. If the surface has an area of 30cm2, the total momentum delivered during 30 minutes is (a) 36 10-5kg m/s (b) 36 10-4kg m/s (c) 108 104kg m/s (d) 1.08 107kg m/s Solution: (b) 36 10-4kg m/s...
Read More →Find the mean deviation about the mean for the following data :
Question: Find the mean deviation about the mean for the following data : Solution: we make the following table from the given data:br data-mce-bogus="1"/ppimg src="https://www.esaral.com/qdb/uploads/2022/02/22/image97539.png" alt="" Therefore, $\overline{\mathrm{X}}=\frac{\sum_{\mathrm{i}=1}^{7} \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\sum_{\mathrm{i}=1}^{7} \mathrm{f}_{\mathrm{i}}}=\frac{3100}{50}=62$...
Read More →A linearly polarized electromagnetic wave given as
Question: A linearly polarized electromagnetic wave given as $E=E_{0} \hat{i} \cos (k z-\omega t) \quad$ is incident normally on a perfectly reflecting infinite wall at $\mathrm{z}=\mathrm{a}$ Assuming that the material of the wall is optically inactive, the reflected wave will be given as (a) $E_{r}=-E_{0} \hat{i} \cos (k z-\omega t)$ (b) $E_{r}=E_{0} \hat{i} \cos (k z+\omega t)$ (c) $E_{r}=-E_{0} \hat{i} \cos (k z+\omega t)$ (d) $E_{r}=E_{0} \hat{i} \sin (k z-\omega t)$ Solution: (b) $E_{r}=E_...
Read More →One requires 11eV of energy to dissociate
Question: One requires 11eV of energy to dissociate a carbon monoxide molecule into carbon and oxygen atoms. The minimum frequency of the appropriate electromagnetic radiation to achieve the dissociation lies in (a) visible region (b) infrared region (c) ultraviolet region (d) microwave region Solution: (c) ultraviolet region...
Read More →Find the mean deviation about the mean for the following data :
Question: Find the mean deviation about the mean for the following data : Solution: we make the following table from the given data:br data-mce-bogus="1"/ppimg src="https://www.esaral.com/qdb/uploads/2022/02/22/image94936.png" alt="" thereforce $\overline{\mathrm{X}}=\frac{\sum_{\mathrm{i}=1}^{7} \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\sum_{\mathrm{i}=1}^{7} \mathrm{f}_{\mathrm{i}}}$ $\frac{3100}{50}=62$...
Read More →In the LCR circuit the ac driving voltage is v = vm sin ωt.
Question: In the LCR circuit the ac driving voltage is v = vm sin t. (i) Write down the equation of motion for q (t). (ii) At t = t0, the voltage source stops and R is short-circuited. Now write down how much energy is stored in each of L and C. (iii) Describe subsequent motion of charges. Solution: (i) The equation for variation of motion of charge with respect to time is given as L d2q(t)/dt + R dq(t)/dt + q(t)/C = Vmsin t (ii) The energy stored in each of L and C is given as Uc = 1/2C2[Vm2/R2...
Read More →Find the mean deviation about the mean for the following data :
Question: Find the mean deviation about the mean for the following data : Solution: we make the following table from the given data:br data-mce-bogus="1"/ppimg src="https://www.esaral.com/qdb/uploads/2022/02/22/image34021.png" alt="" Therefore, $\overline{\mathrm{X}}=\frac{\sum_{\mathrm{i}=1}^{7} \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\sum_{\mathrm{i}=1}^{7} \mathrm{f}_{\mathrm{i}}}=\frac{3100}{50}=62$...
Read More →Evaluate the integral:
Question: Evaluate the integral: $\int \frac{x-3}{x^{2}+2 x-4} d x$ Solution: $I=\int \frac{x-3}{x^{2}+2 x-4} d x$ As we can see that there is a term of $x$ in numerator and derivative of $x^{2}$ is also $2 x$. So there is a chance that we can make substitution for $x^{2}+2 x-4$ and I can be reduced to a fundamental integration. As, $\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{x}^{2}+2 \mathrm{x}-4\right)=2 \mathrm{x}+2$ $\therefore$ Let, $x-3=A(2 x+2)+B$ $\Rightarrow x-3=2 A x+2 A+B$ On compari...
Read More →For an LCR circuit driven at frequency ω,
Question: For an LCR circuit driven at frequency , the equation reads L di/dt + Ri + q/C = vi = vm sin ꞷ t (i) Multiply the equation by i and simplify where possible. (ii) Interpret each term physically. (iii) Cast the equation in the form of a conservation of energy statement. (iv) Integrate the equation over one cycle to find that the phase difference between v and i must be acute. Solution: L di/dt + Ri + q/C = vi = vm sin ꞷ t (i) Multiplying the above equation with I, we get d(1/2 Li2)/dt + ...
Read More →Consider the LCR circuit such that the net current
Question: Consider the LCR circuit such that the net current i and the phase of i. Show that i = V/Z . Find the impedance Z for this circuit. Solution: The impedance Z for the given circuit is given as: 1/Z = [1/R2+ 1/(1/ꞷC ꞷL)2]1/2...
Read More →1MW power is to be delivered from a power station
Question: 1MW power is to be delivered from a power station to a town 10 km away. One uses a pair of Cu wires of radius 0.5 cm for this purpose. Calculate the fraction of ohmic losses to power transmitted if (i) power is transmitted at 220V. Comment on the feasibility of doing this. (ii) a step-up transformer is used to boost the voltage to 11000 V, power transmitted, then a step-down transformer is used to bring the voltage to 220 V. Solution: (i) The power station is 10 km away from the town L...
Read More →An electrical device draws 2kW power from AC mains (voltage 223V (rms) = 50,000 V).
Question: An electrical device draws 2kW power from AC mains (voltage 223V (rms) = 50,000 V). The current differs (lags) in phase by (tan = -3/4) as compared to voltage. Find (i) R, (ii) XC XL, and (iii) IM. Another device has twice the values for R, XC and XL. How are the answers affected? Solution: Impedance = Z = 25 ohms 635 = 25R2/16 (a) Resistance = R = 25 16 = 400 = 20 ohms (b) Xc Xl = -3R/4 = -15 ohms (c) Main current = Im = 12.6 A...
Read More →Find the mean deviation about the mean for the following data
Question: Find the mean deviation about the mean for the following data Solution: we make the following table from the given data: Therefore $\overline{\mathrm{X}}=\frac{\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}}}$ $\frac{12500}{100}=125$...
Read More →Explain why the reactance offered
Question: Explain why the reactance offered by an inductor increases with increasing frequency of an alternating voltage. Solution: The reactance offered by an inductor increases with increasing frequency of an alternating voltage because the induced emf is proportional to the rate of change of current....
Read More →Explain why the reactance provided
Question: Explain why the reactance provided by a capacitor to an alternating current decreases with increasing frequency. Solution: The reactance provided by a capacitor to an alternating current decreases with increasing frequency because capacitance reactance is inversely proportional to the frequency and capacitors have the tendency to pass high-frequency current and to block low-frequency currents....
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