A wire of length 1m and radius 0.1mm has a resistance of 100Ω.
Question: A wire of length $1 \mathrm{~m}$ and radius $0.1 \mathrm{~mm}$ has a resistance of $100 \Omega$. Find the resistivity of the material. Solution:...
Read More →A current of 1.0 A exists in a copper wire of cross-section
Question: A current of $1.0$ A exists in a copper wire of cross-section $1.0 \mathrm{~mm}^{2}$. Assuming one free electron per atom calculate the drift speed of the free electrons in the wire. The density of copper is $9000 \mathrm{~kg} / \mathrm{m}^{3}$. Solution:...
Read More →The current through a wire depends on time as
Question: The current through a wire depends on time as $i=i_{0}+\alpha t$, Solution:...
Read More →The electric current existing in a discharge tube is
Question: The electric current existing in a discharge tube is $2.0 \mu \mathrm{A}$. How much charge is transferred across a cross-section of the tube in 5 minutes? Solution:...
Read More →An electron gun emits
Question: An electron gun emits $2.0 \times 10^{16}$ ele electrons per second. What electric current does this correspond to? Solution:...
Read More →The amount of charge passed in time t through
Question: The amount of charge passed in time $t$ through a cross-section of a wire is $Q(t)=A t^{2}+B t+C .$ (a) Write the dimensional formulae for A, B and C. (b) If the numerical value of $A, B$ and $C$ are 5,3 and 1 respectively in SI units, find the value of current at $t=5 s$. Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when $x=a(1-\cos \theta), y=a(\theta+\sin \theta)$ Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when $x=a \cos ^{3} \theta, y=a \sin ^{3} \theta$ Solution:...
Read More →Consider the situation shown in figure.
Question: Consider the situation shown in figure. The plates of the capacitor have plate area A and are clamped in the laboratory. The dielectric slab is released from rest with a length a inside the capacitor. Neglecting any effect of friction or gravity, show that the slab will execute periodic motion and find its time period. Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when $x=a \cos ^{2} \theta, y=b \sin ^{2} \theta$ Solution:...
Read More →Figure shows two parallel plate capacitors with fixed plates
Question: Figure shows two parallel plate capacitors with fixed plates and connected to two batteries. The separation between the plates is the same for the two capacitors. The plates are rectangular in shape with width $\mathrm{b}$ and length $\mathrm{I}_{1}$ and $\mathrm{I}_{2}$. The left half of the dielectric slab has a dielectric constant $\mathrm{K}_{1}$ and the right half $\mathrm{K}_{2}$. Neglecting any friction, find the ratio of the emf of the left battery to that of the right battery ...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when $x=a \cos \theta, y=b \sin \theta$ Solution:...
Read More →Consider the situation shown in figure.
Question: Consider the situation shown in figure. The width of each plate is $b$. The capacitor plates are rigidly clamped in the laboratory and connected to a battery of emf. All surface are frictionless. Calculate the value of $\mathrm{M}$ for which the dielectric slab will stay in equilibrium. Solution:...
Read More →A parallel-plate capacitor with the plate area
Question: A parallel-plate capacitor with the plate area $100 \mathrm{~cm}^{2}$ and the separation between the plates $1.0 \mathrm{~cm}$ is connected across a battery of emf 24 volts. Find the force of attraction between the plates. Solution:...
Read More →An air filled parallel-plate capacitor is to be constructed
Question: An air filled parallel-plate capacitor is to be constructed which can store $12 \mu \mathrm{C}$ of charge when operated at $1200 \mathrm{~V}$. What can be the minimum plate area of the capacitor? The dielectric strength of air $3 \times 10^{6} \mathrm{~V} / \mathrm{m}$. Solution:...
Read More →Suppose the space between the two inner shells of the previous problem
Question: Suppose the space between the two inner shells of the previous problem is filled with a dielectric of dielectric constant K. Find the capacitance of the system between $A$ and $B$. Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when $x=a t^{2}, y=2 a t$ Solution:...
Read More →Consider an assembly of three conducting concentric spherical shells
Question: Consider an assembly of three conducting concentric spherical shells of radii $a, b$ and $c$ as shown in figure, Find the capacitance of the assembly between the points $A$ and $B$. Solution:...
Read More →The two square faces of a rectangular dielectric slab
Question: The two square faces of a rectangular dielectric slab (dielectric constant 4.0) of dimensions $20 \mathrm{~cm} \times 20 \mathrm{~cm} \times 1.0 \mathrm{~mm}$ are metal-coated. Find the capacitance between the coated surfaces. Solution:...
Read More →A 5.0 μF capacitor is charged to 12 V.
Question: A $5.0 \mu \mathrm{F}$ capacitor is charged to $12 \mathrm{~V}$. The positive plate of this capacitor is now connected to the negative terminal of a $12 \mathrm{~V}$ battery and vice versa. Calculate the heat developed in the connecting wires." Solution:...
Read More →A capacitor of capacitance 5.00 μF is charged to 24.0 V
Question: A capacitor of capacitance $5.00 \mu \mathrm{F}$ is charged to $24.0 \mathrm{~V}$ and another capacitor of capacitance 6 ' $0 \mu \mathrm{F}$ is charged to $12.0 \mathrm{~V}$. (a) Find the energy stored in each capacitor, (b) The positive plate of the first capacitor is now connected to the negative plate of the second and vice versa. Find the. new charges on the capacitors, (c) Find the loss of electrostatic energy during the process, (d) Where does this energy go ? Solution:...
Read More →Solve this following
Question: Differentiate $\tan ^{-1}\left(\frac{\sqrt{1-x^{2}}}{x}\right)$ with respect to $\cos ^{-1}\left(2 x \sqrt{1-x^{2}}\right)$ when $x \neq 0$ Solution:...
Read More →A spherical capacitor is made of two conducting spherical shells of radii a and b.
Question: A spherical capacitor is made of two conducting spherical shells of radii a and $b$. The space between the shells is filled with a dielectric of dielectric constant $\mathrm{K}$ up to a radius $\mathrm{c}$ as shown in figure Calculate the capacitance. Solution:...
Read More →A capacitor having a capacitance of 100 μF is charged to a potential difference of 50 V.
Question: A capacitor having a capacitance of $100 \mu \mathrm{F}$ is charged to a potential difference of $50 \mathrm{~V}$. (a) What is the magnitude of the charge on each plate? (b) The charging battery is disconnected and a dielectric of dielectric constant $2.5$ is inserted. Calculate the new potential difference between the plates, (c) What charge would have produced this potential .difference in absence of the dielectric slab, (d) Find the charge induced at a surface of the dielectric slab...
Read More →A parallel-plate capacitor of plate area A and plate separation d
Question: A parallel-plate capacitor of plate area $\mathrm{A}$ and plate separation $\mathrm{d}$ is charged to a potential difference $\mathrm{V}$ and then the battery is disconnected. A slab of dielectric constant $\mathrm{K}$ is then inserted between the plates of the capacitor so as to fill the space between the plates. Find the work done on the system in the process of inserting the slab. Solution:...
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