A coil has a resistance of 10Ω and an inductance of 0.4 henry.
Question: A coil has a resistance of $10 \Omega$ and an inductance of $0.4$ henry. It is connected to an Ac source of $6.5 \mathrm{~V}$, $\frac{30}{\pi} \mathrm{Hz}$. Find the average power consumed in the circuit. Solution:...
Read More →A coil of inductance 5.0mH and negligible resistance is connected
Question: A coil of inductance $5.0 \mathrm{mH}$ and negligible resistance is connected to the oscillator of the previous problem. Find the peak currents in the circuit for $\omega=100 \mathrm{~s}^{-1}, 500 \mathrm{~s}^{-1}, 1000 \mathrm{~s}^{-1}$. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=\log \left(\frac{\sqrt{1+x^{2}}+x}{\sqrt{1+x^{2}}-x}\right)$ then $\frac{d y}{d x}=$ ? A. $\frac{2}{\sqrt{1+x^{2}}}$ B. $\frac{2 \sqrt{1+x^{2}}}{x^{2}}$ C. $\frac{-2}{\sqrt{1+\mathrm{x}^{2}}}$ D. none of these Solution:...
Read More →A capacitor of capacitance 10µF is connected to an oscillator giving an
Question: A capacitor of capacitance $10 \mu \mathrm{F}$ is connected to an oscillator giving an output voltage $\varepsilon=(10 \mathrm{~V}) \sin \omega \mathrm{t}$. Find the peak currents in the circuit for $\omega=10 \mathrm{~s}^{-1}, 100 \mathrm{~s}^{-1}, 500 \mathrm{~s}^{-1}, 1000 \mathrm{~s}^{-1}$. Solution:...
Read More →The current in the discharging LR circuit is given by
Question: The current in the discharging LR circuit is given by $\mathrm{i}=\mathrm{i}_{0} \mathrm{e}^{-\mathrm{t} / \tau}$ where $T$ is the time constant of the circuit. Calculate the rms current for the period $t=0$ to $t=T$. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in the following: If $y=\log \left(\frac{1+\sqrt{x}}{1-\sqrt{x}}\right)$ then $\frac{d y}{d x}=?$ A. $\frac{1}{\sqrt{x}(1-x)}$ B. $\frac{-1}{x(1-\sqrt{x})^{2}}$ C. $\frac{-\sqrt{x}}{2(1-\sqrt{x})}$ D. none of these Solution:...
Read More →The dielectric strength of air is
Question: The dielectric strength of air is $3.0 \times 10^{6} \mathrm{~V} / \mathrm{m}$. A parallel-plate air-capacitor has area $20 \mathrm{~cm}^{2}$ and plate separation $0.10 \mathrm{~mm}$. Find the maximum rms voltage of an AC source which can be safely connected to this capacitor. Solution:...
Read More →The peak power consumed by a resistive coil when connected to an AC
Question: The peak power consumed by a resistive coil when connected to an AC source is $80 \mathrm{~W}$. Find the energy consumed by the coil in 100 seconds which is many times larger than the time period of the source. Solution:...
Read More →An electric bulb is designed to operate at 12 volts DC.
Question: An electric bulb is designed to operate at 12 volts DC. If this bulb is connected to an AC source and gives normal brightness, what would be the peak voltage of the source? Solution:...
Read More →A bulb rated 60W at 220V is connected across a household supply of
Question: A bulb rated $60 \mathrm{~W}$ at $220 \mathrm{~V}$ is connected across a household supply of alternating voltage of $220 \mathrm{~V}$. Calculate the maximum instantaneous current through the filament. Solution:...
Read More →The household supply of electricity is at 220V (rms value)
Question: The household supply of electricity is at $220 \mathrm{~V}$ (rms value) and $50 \mathrm{~Hz}$. Find the peak voltage and the least possible time in which the voltage can change from the rms value to zero. Solution:...
Read More →Find the time required for a 50Hz alternating current to change
Question: Find the time required for a $50 \mathrm{~Hz}$ alternating current to change its value from zero to the rms value. Solution:...
Read More →The current in a long solenoid of radius
Question: The current in a long solenoid of radius $\mathrm{R}$ having $\mathrm{n}$ turns per unit length is given by $i=i_{0} \sin \omega t$. A coil having $\mathrm{N}$ turns is wound around it near the center. Find (a) the induced emf in the coil and (b) the mutual inductance between the solenoid and the coil. Solution:...
Read More →A solenoid of length 20cm,
Question: A solenoid of length $20 \mathrm{~cm}$, area of cross-section $4.0 \mathrm{~cm}^{2}$ and having 4000 turns is placed inside another solenoid of 2000 turns having a cross-sectional area $8.0 \mathrm{~cm}^{2}$ and length $10 \mathrm{~cm}$. Find the mutual inductance between the solenoids. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=\log \left(x+\sqrt{x^{2}+a^{2}}\right)$ then $\frac{d y}{d x}=?$ A. $\frac{1}{2\left(x+\sqrt{x^{2}+a^{2}}\right)}$ B. $\frac{-1}{\sqrt{x^{2}+a^{2}}}$ C. $\frac{1}{\sqrt{x^{2}+a^{2}}}$ D. none of these Solution:...
Read More →Find the mutual inductance between the circular coil and the loop shown in figure.
Question: Find the mutual inductance between the circular coil and the loop shown in figure. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=\cos ^{2} x^{3}$ then $\frac{d y}{d x}=$ ? A. $-3 x^{2} \sin$ B. $-3 x^{2} \sin ^{2} x^{3}$ C. $-3 x^{2} \cos ^{2}\left(2 x^{3}\right)$ D. none of these Solution:...
Read More →Find the mutual inductance between the straight wire and the square of the figure.
Question: Find the mutual inductance between the straight wire and the square of the figure. Solution:...
Read More →The mutual inductance between two coils is
Question: The mutual inductance between two coils is $2.5 \mathrm{H}$. If the current in one coil is changed at the rate of $1 \mathrm{~A} / \mathrm{s}$, what will be the emf induced in the other coil? Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=x^{2} \sin \frac{1}{x}$ then $\frac{d y}{d x}=?$ A. $x \sin \frac{1}{x}-\cos \frac{1}{x}$ B. $-\cos \frac{1}{x}+2 x \sin \frac{1}{x}$ C. $-x \sin \frac{1}{x}+\cos \frac{1}{x}$ D. None of these Solution:...
Read More →A long wire carries a current of 4.00A.
Question: A long wire carries a current of $4.00 \mathrm{~A}$. Find the energy stored in the magnetic field inside a volume of $1.00 \mathrm{~mm}^{3}$ at a distance of $10.0 \mathrm{~cm}$ from the wire. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $x^{p} y^{q}=(x+y)^{(p+q)}$ then $\frac{d y}{d x}=?$ A. $\frac{\mathrm{x}}{\mathrm{y}}$ B. $\frac{y}{x}$ C. $\frac{x^{p-1}}{y^{q-1}}$ D. none of these Solution:...
Read More →A current of 1.0A is established in a tightly wound solenoid of radius 2cm
Question: A current of $1.0 \mathrm{~A}$ is established in a tightly wound solenoid of radius $2 \mathrm{~cm}$ having 1000 turns/meter. Find the magnetic energy stored in each meter of the solenoid. Solution:...
Read More →Consider the circuit shown in figure.
Question: Consider the circuit shown in figure. (a) Find the current through the battery a long time after the switch $\mathrm{S}$ is closed. (b) Suppose the switch is again opened at $\mathrm{t}=0$. What is the time constant of the discharging circuit? (c) Find the current through the inductor after one time constant. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in the following: If $x^{y}=y^{x}$ then $\frac{d y}{d x}=$ ? A. $\frac{(y-x \log y)}{(x-y \log x)}$ B. $\frac{y(y-x \log y)}{x(x-y \log x)}$ C. $\frac{y(y+x \log y)}{x(x+y \log x)}$ D. none of these Solution:...
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