A parallel-plate capacitor having plate area 20cm squer and separation between
Question: A parallel-plate capacitor having plate area $20 \mathrm{~cm}^{2}$ and separation between the plates $\mathrm{l} .00 \mathrm{~mm}$ is connected to a battery of $12.0 \mathrm{~V}$. The plates are pulled apart to increase the separation to $2.0 \mathrm{~mm}$. (a) Calculate the charge flown through the circuit during the process, (b) How much energy is absorbed by the battery during the process? (c) Calculate the stored energy in the electric field before and after the process, (d) Using ...
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Question: If $\mathrm{y}=\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\ldots \infty}}}$, prove that $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{(2 \mathrm{y}-1)}$. Solution:...
Read More →A large conducting plane has a surface charge density
Question: A large conducting plane has a surface charge density $1.0 \times 10^{-4} \mathrm{C} / \mathrm{m}^{2}$ Find the electrostatic energy stored in a cubical volume of edge $1.0 \mathrm{~cm}$ in front of the plane. Solution:...
Read More →A metal sphere of radius R is charged to a potential V.
Question: A metal sphere of radius $\mathrm{R}$ is charged to a potential $\mathrm{V}$. (a) Find the electrostatic energy stored in the electric field within a concentric sphere of radius $2 \mathrm{R}$. (b) Show that the electrostatic field energy stored outside the sphere of radius $2 \mathrm{R}$ equals that stored within it. Solution: hence proved...
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Question: Solution: Differentiating both sides with respect to $x$...
Read More →A point charge Q is placed at the origin.
Question: A point charge $Q$ is placed at the origin. Find the electrostatic energy stored outside the sphere of radius $R$ centred at the origin. Solution:...
Read More →A capacitor of capacitance 2 0 μF is charged to a potential difference of
Question: A capacitor of capacitance $20 \mu \mathrm{F}$ is charged to a potential difference of $12 \mathrm{~V}$. It is then connected to an uncharged capacitor of capacitance $4^{\prime} 0 \mu \mathrm{F}$ as shown in figure (31-E22). Find (a) the charge on each of the two capacitors after the connection, (b) the electrostatic energy stored in each of the two capacitors and (c) the heat produced during the charge transfer from one capacitor to the other. Solution:...
Read More →A capacitor with stored energy 4.0 J is connected with
Question: A capacitor with stored energy $4.0 \mathrm{~J}$ is connected with an identical capacitor with no electric field in between. Find the total energy stored in the two capacitors. Solution:...
Read More →Each capacitor in figure has a capacitance of
Question: Each capacitor in figure has a capacitance of $10 \mu \mathrm{F}$. The emf of the battery is $100 \mathrm{~V}$. Find the energy stored in each of the four capacitors. Solution:...
Read More →Two capacitors of capacitances 4.0 μ F and 6.0 μF
Question: Two capacitors of capacitances $4.0 \mu \mathrm{F}$ and $6.0 \mu \mathrm{F}$ are connected in series with a battery of $20 \mathrm{~V}$. Find the energy supplied by the battery. Solution:...
Read More →Two capacitors of capacitances 20.0 pF and 50.0 pF
Question: Two capacitors of capacitances $20.0 \mathrm{pF}$ and $50.0 \mathrm{pF}$ are connected in series with a $6.00 \mathrm{~V}$ battery. Find (a) the potential difference across each capacitor and (b) the energy stored in each capacitor. Solution:...
Read More →Consider the situation of the previous problem.
Question: Consider the situation of the previous problem. If $\mathrm{I} .0 \mu \mathrm{C}$ is placed on the upper plate instead of the middle, what will be the potential difference between (a) the upper and the middle plates and (b) the middle and the lower plates? Solution:...
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Question: If $x^{m} y^{n}=(x+y)^{m+n}$, prove that $\frac{d y}{d x}=\frac{y}{x}$ Solution:...
Read More →The capacitance between the adjacent plates shown in figure is
Question: The capacitance between the adjacent plates shown in figure is $50 \mathrm{nF}$. A charge of I.0 $\mu \mathrm{C}$ is placed on the middle plate, (a) What will be the charge on the outer surface of the upper plate? (b) Find the potential difference developed between the upper and the middle plates. Solution:...
Read More →Each of the plates shown in figure has surface area
Question: Each of the plates shown in figure has surface area $\left(96 / \varepsilon_{0}\right) \times 10^{-1} F-m$ on one side and the separation between the consecutive plates is $4.0 \mathrm{~mm}$. The emf of the battery connected is 10 volts. Find the magnitude of the charge supplied by the battery to each of the plates connected to it. Solution:...
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Question: Find, when: If $y=\tan ^{-1} \frac{a}{x}+\log \sqrt{\frac{x-a}{x+a}}$, prove that $\frac{d y}{d x}=\frac{2 a^{3}}{\left(x^{4}-a^{4}\right)}$ Solution:...
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Question: $y=x^{\cot x}+\frac{2 x^{2}-3}{x^{2}+x+2}$, find $\frac{d y}{d x}$ Solution:...
Read More →A charge of 1 μC is given to one plate of
Question: A charge of $1 \mu \mathrm{C}$ is given to one plate of a parallel-plate capacitor of capacitance $0.1 \mu \mathrm{F}$ and a charge of $2 \mu \mathrm{C}$ is given to the other plate. Find the potential difference developed between the plates. Solution:...
Read More →A charge of 20 micro coloumb is placed on the positive
Question: A charge of 20 micro coloumb is placed on the positive plate of an isolated parallel-plate capacitor of capacitance 10 microfarad. Calculate the potential difference developed between the plates. Solution:...
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Question: If $\left(x^{2}+y^{2}\right)^{2}=x y$, find $\frac{d y}{d x}$ Solution:...
Read More →A charge of
Question: A charge of $+2.0 \times 10^{-8} \mathrm{C}$ is placed on the positive plate and a charge of $-1.0 \times 10^{-8} \mathrm{C}$ on the negative plate of a parallel-plate capacitor of capacitance $1.2 \times 10^{-3} \mu \mathrm{F}$. Solution:...
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Question: If $y=(\sin x)^{x}+\sin ^{-1} \sqrt{x}$, find $\frac{d y}{d x}$ Solution:...
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Question: If $f(x)=\left(\frac{3+x}{1+x}\right)^{2+3 x}$, find $f^{\prime}(0)$ Solution:...
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Question: If $y-x\left(x^{2}-3\right)+(x-3)^{x^{2}}$, find $\frac{d y}{d x}$ Solution:...
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