A Capacitor is made of a flat plate of area
Question: A Capacitor is made of a flat plate of area $\mathrm{A}$ and a second plate having a stair-like structure as shown in figure. The width of each stair is a and the height is $b$. Find the capacitance of the assembly. Solution:...
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Question: If $\mathrm{x}^{\mathrm{a}} \mathrm{y}^{\mathrm{b}}=(\mathrm{x}+\mathrm{y})^{(\mathrm{a}+\mathrm{b})}$, prove that $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{y}}{\mathrm{x}}$ Solution:...
Read More →Find the equivalent capacitance of the system shown in
Question: Find the equivalent capacitance of the system shown in figure between the points a and $b$. Solution:...
Read More →Take the potential of the point B in figure to be zero.
Question: Take the potential of the point B in figure to be zero. (a) Find the potentials at the points $C$ and D. (b) If a capacitor is connected between $C$ and $D$, what charge will appear on this capacitor? Solution:...
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Question: If $\mathrm{y}=\sqrt{\mathrm{x}+\mathrm{y}}$, prove that $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{(2 \mathrm{y}-1)}$. Solution:...
Read More →It is required to construct a 10μF capacitor
Question: It is required to construct a $10 \mu \mathrm{F}$ capacitor which can be connected across a $200 \mathrm{~V}$ battery. Capacitors of capacitance $10 \mu \mathrm{F}$ are available but they can withstand only $50 \mathrm{~V}$. Design a combination which can yield the desired result. Solution:...
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Question: If $y=\frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}$, prove that $\left(1-x^{2}\right) \frac{d y}{d x}=(x y+1)$ Solution:...
Read More →Each of the capacitors shown in figure has a capacitance of
Question: Each of the capacitors shown in figure has a capacitance of $2 \mu \mathrm{F}$. Find the equivalent capacitance of the assembly between the points A and B. Find the potential difference appearing on the individual capacitors. Solution:...
Read More →Two conducting spheres of radii R1and R2
Question: Two conducting spheres of radii $\mathrm{R}_{1}$ and $\mathrm{R}_{2}$ are kept widely separated from each other. What are their individual capacitance? If the spheres are connected by a metal wire, what will be the capacitance of the combination? Think in terms of series parallel connections. Solution:...
Read More →The outer cylinders of two cylindrical capacitors of capacitance
Question: The outer cylinders of two cylindrical capacitors of capacitance $2.2 \mu \mathrm{F}$ each, are kept in contact and the inner cylinders are connected through a wire. A battery of emf $10 \mathrm{~V}$ connected as shown in figure. Find the total charge supplied by the battery to the inner cylinders. Solution:...
Read More →Find the charge supplied by the battery in the arrangement shown in figure
Question: Find the charge supplied by the battery in the arrangement shown in figure Solution:...
Read More →Take C1=4.0μF and C2=6.0μF in figure.
Question: Take $C_{1}=4.0^{\mu} \mathrm{F}$ and $C_{2}=6.0 \mu \mathrm{F}$ in figure. Calculate the equivalent capacitance of the combination between the points indicated. Solution:...
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Question: Find $\frac{\mathrm{dy}}{\mathrm{dx}}$, when: $y=\left((\log x)^{x}+(x)^{\log x}\right.$ Solution:...
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Question: Find $\frac{d y}{d x}$, when: $(\tan x)^{y}=(\tan y)^{x}$ Solution:...
Read More →Find the charge appearing on each of the three capacitors shown in figure
Question: Find the charge appearing on each of the three capacitors shown in figure Solution:...
Read More →Three capacitors having capacitances
Question: Three capacitors having capacitances $20 \mu \mathrm{F}, 30 \mu \mathrm{F}$ and $40 \mu \mathrm{F}$ are connected in series with a $12 \mathrm{~V}$ battery. Find the charge on each capacitor. How much work has been done by the battery in charging the capacitors? Solution:...
Read More →Find the charges on the three capacitors connected to a battery as shown in figure.
Question: Find the charges on the three capacitors connected to a battery as shown in figure. Takes, $C_{1}=2.0 \mu F, C_{2}=4.0 \mu F C_{3}=6.0 \mu F$ and $V=12$ volt. Solution: Potential difference across each capacitor is $\mathrm{V}$ as all are in parallel combination....
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Question: Find $\frac{d y}{d x}$, when: $(\cos x)^{y}=(\cos y)^{x}$ Solution:...
Read More →A parallel plate capacitor has plate area
Question: A parallel plate capacitor has plate area $25.0 \mathrm{~cm}^{2}$ and a separation of $2.00 \mathrm{~mm}$ between the plates. The capacitor is connected to a battery of $12.0 \mathrm{~V}$ (a) Find the charge on the capacitor. (b) The plate separations decreased to $1.00 \mathrm{~mm}$. Find the extra charge given by the battery to the positive plate. Solution:...
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Question: Find $\frac{d y}{d x}$, when: $y=(2 x+3)^{5}(3 x-5)^{7}(5 x-1)^{3}$ Solution:...
Read More →A parallel-plate capacitor having plate area
Question: A parallel-plate capacitor having plate area $25 \mathrm{~cm}^{2}$ and separation $1.00 \mathrm{~mm}$ is connected to a battery of $6.0 \mathrm{~V}$. Calculate the charge flown through the battery. How much work has been done by the battery during the process? Solution:...
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Question: Find $\frac{d y}{d x}$, when: $y=x^{x} \cdot e^{(2 x+5)}$ Solution:...
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Question: Find $\frac{d y}{d x}$, when: $y=2^{x} \cdot e^{3 x} \sin 4 x$ Solution:...
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Question: Find $\frac{d y}{d x}$, when: $y=e^{x} \sin ^{3} x \cos ^{4} x$ Solution:...
Read More →Suppose, one wishes to construct a 1.0 farad capacitor using circular discs.
Question: Suppose, one wishes to construct a $1.0$ farad capacitor using circular discs. If the separation between the discs be kept at $1.0 \mathrm{~mm}$, what would be the radius of the discs? Solution:...
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