Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in the following: If $y=\sin ^{-1}\left\{\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right\}$ then $\frac{d y}{d x}=?$ A. $\frac{-1}{2 \sqrt{1-x^{2}}}$ B. $\frac{1}{2 \sqrt{1-x^{2}}}$ C. $\frac{1}{2 \sqrt{1+x^{2}}}$ D. none of these Solution:...
Read More →The plate current in a diode is 20mA when the plate voltage is 50V or 60V.
Question: The plate current in a diode is $20 \mathrm{~mA}$ when the plate voltage is $50 \mathrm{~V}$ or $60 \mathrm{~V}$. What will be the current if the plate voltage is $70 \mathrm{~V}$ ? Solution: Plate have voltage of $50 \mathrm{~V}$ or $60 \mathrm{~V}$, so its acts as saturation current. Hence, for other value of voltages current is $20 \mathrm{~mA}$....
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=\tan ^{-1}\left\{\frac{\sqrt{1+x^{2}-1}}{x}\right\}$ then $\frac{d y}{d x}=?$ A. $\frac{1}{\left(1+x^{2}\right)}$ B. $\frac{2}{\left(1+x^{2}\right)}$ C. $\frac{1}{2\left(1+x^{2}\right)}$ D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: If $y=\sec ^{-1}\left(\frac{1}{2 x^{2}-1}\right)$ then $\frac{d y}{d x}=?$ A. $\frac{-2}{\left(1+x^{2}\right)}$ B. $\frac{-2}{\left(1-x^{2}\right)}$ C. $\frac{-2}{\sqrt{1+x^{2}}}$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=\sec ^{-1}\left(\frac{x^{2}+1}{x^{2}-1}\right)$ then $\frac{d y}{d x}=?$ A. $\frac{-2}{\left(1+x^{2}\right)}$ B. $\frac{2}{\left(1+x^{2}\right)}$ C. $\frac{-1}{\left(1+\mathrm{x}^{2}\right)}$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $\mathrm{y}=\sqrt{\frac{1+x}{1-x}}$ then $\frac{d y}{d x}=?$ A. $\frac{2}{(1-x)^{2}}$ B. $\frac{x}{(1-x)^{3 / 2}}$ C. $\frac{1}{(1-x)^{3 / 2} \cdot(1+x)^{1 / 2}}$ D. none of these Solution:...
Read More →A plate current of 10mA is obtained when 60volts are applied across a diode tube.
Question: A plate current of $10 \mathrm{~mA}$ is obtained when 60 volts are applied across a diode tube. Assuming the Langmuir-Child equation $i_{p} \propto V_{p}^{3 / 2}$ to hold, find the dynamic resistance $r_{p}$ in this operating condition. Solution:...
Read More →The constant A in the Richardson-Dushman equation for tungsten
Question: The constant $\mathrm{A}$ in the Richardson-Dushman equation for tungsten $60 \times 10^{4} \frac{\mathrm{A}}{\mathrm{m}^{2}}-\mathrm{K}^{2}$. The work function of tungsten is $4.5 \mathrm{eV}$. A tungsten cathode having a surface are $2.0 \times 10^{-5} \mathrm{~m}^{2}$ is heated by a $24 \mathrm{~W}$ electric heater. In steady state, the heat radiated by the cathode equals the energy input by the heater and the temperature becomes constant. Assuming that the cathode radiates like a b...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=\cot ^{-1}\left(\frac{1-x}{1+x}\right)$ then $\frac{d y}{d x}=?$ A. $\frac{-1}{\left(1+x^{2}\right)}$ B. $\frac{1}{\left(1+x^{2}\right)}$ C. $\frac{-1}{\left(1+x^{2}\right)^{3 / 2}}$ D. none of these Solution:...
Read More →If the temperature of a tungsten filament is raised from
Question: If the temperature of a tungsten filament is raised from $2000 \mathrm{~K}$ to $2010 \mathrm{~K}$, by what factor does the emission current change? Work function of tungsten is $4.5 \mathrm{eV}$. Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=\tan ^{-1}(\sec x+\tan x)$ then $\frac{d y}{d x}=?$ A. $\frac{1}{2}$ B. $\frac{-1}{2}$ C. 1 D. none of these Solution: $\frac{d y}{d x}=\frac{1}{2}$...
Read More →A tungsten cathode and a thoriated-tungsten cathode have same geometrical dimensions and
Question: A tungsten cathode and a thoriated-tungsten cathode have same geometrical dimensions and are operated at the same temperature. The thoriated-tungsten cathode gives 5000 times more current than the other one. Find the operating temperature. Take relevant data from the previous problem. Solution:...
Read More →The saturation current from a thoriated-tungsten cathode at 2000K is 10mA.
Question: The saturation current from a thoriated-tungsten cathode at $2000 \mathrm{~K}$ is $10 \mathrm{~mA}$. What will be the saturation current for puretungsten cathode of the same surface area operating at the same temperature? The constant A in the Richardson-Dushmaan equation is$60 \times \frac{10^{4} \mathrm{~A}}{\mathrm{~m}^{2}}-\mathrm{K}^{2}$for pure tungsten and$3.0 \times \frac{10^{4} \mathrm{~A}}{\mathrm{~m}^{2}}-\mathrm{K}^{2}$ for thoriated tungsten. The work function of pure tung...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=\cos ^{-1} x^{3}$ then $\frac{d y}{d x}=?$ A. $\frac{-1}{\sqrt{1-\mathrm{X}^{6}}}$ B. $\frac{-3 x^{2}}{\sqrt{1-x^{6}}}$ C. $\frac{-3}{x^{2} \sqrt{1-x^{6}}}$ D. none of these Solution:...
Read More →Calculate n(T)/n(1000K) for tungsten emitter at T=300K, 2000K and 3000K
Question: Calculate $\mathrm{n}(\mathrm{T}) / \mathrm{n}(1000 \mathrm{~K})$ for tungsten emitter at $\mathrm{T}=300 \mathrm{~K}, 2000 \mathrm{~K}$ and $3000 \mathrm{~K}$ where $\mathrm{n}(\mathrm{T})$ represents the number of thermions emitted per second by the surface at temperature $T$. Work function of tungsten is $4.52 \mathrm{eV}$. Solution:...
Read More →Two discharge tubes have identical material structure and the same gas is filled in them.
Question: Two discharge tubes have identical material structure and the same gas is filled in them. The length of one tube is $10 \mathrm{~cm}$ and that of the other tube is $20 \mathrm{~cm}$. Sparking starts in both the tubes when the potential difference between the cathode and anode is $100 \mathrm{~V}$. If the pressure in the shorter tube is $1.0 \mathrm{~mm}$ of mercury, what is the pressure in the longer tube? Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: If $y=\tan ^{-1}\left(\frac{1+x^{2}}{1-x^{2}}\right)$ then $\frac{d y}{d x}=?$ A. $\frac{2 x}{\left(1+x^{4}\right)}$ B. $\frac{-2 x}{\left(1+x^{4}\right)}$ C. $\frac{\mathrm{x}}{\left(1+\mathrm{x}^{4}\right)}$ D. none of these Solution:...
Read More →The mean free path of electrons in the gas in a discharge
Question: The mean free path of electrons in the gas in a discharge tube is inversely proportional to the pressure inside it. The crookes dark space occupies half the length of the discharge tube when the pressure is $0.02 \mathrm{~mm}$ of mercury. Estimate the pressure at which the dark space will fill the whole tube. Solution:...
Read More →A molecule of a gas, filled in a discharge tube,
Question: A molecule of a gas, filled in a discharge tube, gets ionized when an electron is detached from it. An electric field of $5.0 \mathrm{kV} / \mathrm{m}$ exists in the vincinity of the event. (a) Find the distance travelled by the free electron in $1 \mu_{\mathrm{S}}$ assuming no collision. (b) If the mean free path of the electron is $1.0 \mathrm{~mm}$, estimate the time of transit of the free electron between successive collisions. Solution:...
Read More →A discharge tube contains helium at a low pressure.
Question: A discharge tube contains helium at a low pressure. A large potential difference is applied across the tube. Consider a helium atom that has just been ionized due to the detachment of an atomic electron. Find the ratio of the distance travelled by the free electron to that by the free electron to that by the positive ion in a short time dt after the ionization. Solution:...
Read More →Mark against the correct answer in the following:
Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=\cos ^{-1}\left(\frac{x^{2}-1}{x^{2}+1}\right)$ then $\frac{d y}{d x}=?$ A. $\frac{2}{\left(1+x^{2}\right)}$ B. $\frac{-2}{\left(1+x^{2}\right)}$ C. $\frac{2 \mathrm{x}}{\left(1+\mathrm{x}^{2}\right)}$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=\tan ^{-1}\left(\frac{\sqrt{a}+\sqrt{x}}{1-\sqrt{a x}}\right)$ then $\frac{d y}{d x}=?$ A. $\frac{1}{(1+\mathrm{x})}$ B. $\frac{1}{\sqrt{x}(1+x)}$ C. $\frac{2}{\sqrt{x}(1+x)}$ D. $\frac{1}{2 \sqrt{x}(1+x)}$ Solution:...
Read More →The intensity of the sunlight reaching the earth is
Question: The intensity of the sunlight reaching the earth is $1380 \mathrm{~W} / \mathrm{m}^{2}$. Assume this light to be a plane, monochromatic wave, Find the amplitude of electric and magnetic fields in this wave. Solution:...
Read More →A laser beam has intensity
Question: A laser beam has intensity $2.5 \times 10^{14} \mathrm{~W} / \mathrm{m}^{2}$. Find the amplitudes of electric and magnetic fields in the beam. Solution:...
Read More →The magnetic field in a plane electromagnetic wave is given by
Question: The magnetic field in a plane electromagnetic wave is given by $B=(200 \mu T) \sin \left[\left(4.0 \times 10^{15} s^{-1}\right)(t-x / c)\right]$ Find the maximum electric field and the average energy density corresponding to the electric field. Solution:...
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