A constant current exists in an inductor-coil connected to a battery.
Question: A constant current exists in an inductor-coil connected to a battery. The coil is short-circuited and the battery is removed. Show that the charge flown through the coil after the short-circuiting is the same as that which flows in one time constant before the short-circuiting. Solution:...
Read More →An inductor-coil of inductance 17mH is constructed by
Question: An inductor-coil of inductance $17 \mathrm{mH}$ is constructed by a copper wire of length $100 \mathrm{~m}$ and cross-sectional area $1 \mathrm{~mm}{ }^{2}$. Calculate the time constant of the circuit if this inductor is joined across an ideal battery. The resistivity of copper= $1.7 \times 10^{8} \Omega-m$. Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: If $\sqrt{x}+\sqrt{y}=\sqrt{a}$ then $\frac{d y}{d x}=$ ? A. $\frac{-\sqrt{x}}{\sqrt{y}}$ B. $-\frac{1}{2} \cdot \frac{\sqrt{y}}{\sqrt{x}}$ C. $\frac{-\sqrt{y}}{\sqrt{x}}$ D. None of these Solution:...
Read More →An inductor-coil of resistance 10Ω and inductance 120mH
Question: An inductor-coil of resistance $10 \Omega$ and inductance $120 \mathrm{mH}$ is connected across a battery of emf $6 \mathrm{~V}$ and internal resistance $2 \Omega$. Find the charge which flows through the inductor in (a) 10ms, (b) $20 \mathrm{~ms}$ and (c) $100 \mathrm{~ms}$ after the connections are made. Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: If $(x+y)=\sin (x+y)$ then $\frac{d y}{d x}=?$ A. -1 B. 1 C. $\frac{1-\cos (x+y)}{\cos ^{2}(x+y)}$ D. none of these Solution:...
Read More →An LR circuit contains an inductor of
Question: An LR circuit contains an inductor of $500 \mathrm{mH}$, a resistor of $25.0 \Omega$ and an emf of $5.00 \mathrm{~V}$ in series. Find the potential difference across the resistor at (a) $t=$ $20.0 \mathrm{~ms}$, (b) $100 \mathrm{~ms}$ and (c) $1.00 \mathrm{~s}$. Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $e^{x+y}=x y$ then $\frac{d y}{d x}=?$ A. $\frac{x(1-y)}{y(x-1)}$ B. $\frac{y(1-x)}{x(y-1)}$ C. $\frac{(x-x y)}{(x y-y)}$ D. none of these Solution:...
Read More →An inductor-coil of inductance 20mH having resistance 10Ω
Question: An inductor-coil of inductance $20 \mathrm{mH}$ having resistance $10 \Omega$ is joined to an ideal battery of emf $5.0 \mathrm{~V}$. Find the rate of change of the induced emf at (a) $t=0$, (b) $t=10 \mathrm{~ms}$, and (c) $t=1.0 \mathrm{~s}$. Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=\sqrt{x \sin x}$ then $\frac{d y}{d x}=?$ A. $\frac{(x \cos x+\sin x)}{2 \sqrt{x \sin x}}$ B. $\frac{1}{2}(x \cos x+\sin x) \cdot \sqrt{x \sin x}$ C. $\frac{1}{2 \sqrt{x \sin x}}$ D. none of these Solution:...
Read More →What are the values of the self-induced emf in
Question: What are the values of the self-induced emf in the circuit of the previous problem at the times indicated therein? Solution:...
Read More →An LR circuit has L=0.1H and R=20Ω.
Question: An $L R$ circuit has $L=0.1 H$ and $R=20 \Omega$. It is connected across an emf of $2.0 \mathrm{~V}$ at $t=0$. Find di/dt at (a) $t=100 \mathrm{~ms}$, (b) $t=200 \mathrm{~ms}$ and (c) $t=1.0 \mathrm{~s}$. Solution:...
Read More →The time constant of an LR circuit is 40ms.
Question: The time constant of an LR circuit is $40 \mathrm{~ms}$. The circuit is connected at $t=0$ and the steady-current is found to be $2.0 \mathrm{~A}$. Find the current at (a) $t=10 \mathrm{~ms}$, (b) $t=20 \mathrm{~ms}$, (c) $t=100 \mathrm{~ms}$ and (d) $t=1 \mathrm{~s}$. Solution:...
Read More →An inductor of resistance 5.0 H,
Question: An inductor of resistance $5.0 \mathrm{H}$, having a negligible resistance, is connected in series with a $100 \Omega$ resistor and a battery of emf $2.0 \mathrm{~V}$. Find the potential difference across the resistor $20 \mathrm{~ms}$ after the circuit is switched on. Solution:...
Read More →A coil of resistance 40Ω is connected across a 4.0 V battery 0.10s
Question: A coil of resistance $40 \Omega$ is connected across a $4.0 \mathrm{~V}$ battery $0.10$ s after the battery is connected, the current in the coil is $63 \mathrm{~mA}$. Find the inductance of the coil. Solution:...
Read More →A coil having inductance 2.0 H and resistance 20Ω
Question: A coil having inductance $2.0 \mathrm{H}$ and resistance $20 \Omega$ is connected to a battery of emf $4.0 \mathrm{~V}$. Find (a) the current at the instant $0.20$ s after the connection is made and (b) the magnetic field energy at this instant. Solution:...
Read More →An inductor-coil carries a steady-current of
Question: An inductor-coil carries a steady-current of $2.0 \mathrm{~A}$ when connected across an ideal battery of emf $4.0 \mathrm{~V}$. It its inductance is $1.0$ $\mathrm{H}$, find the time constant of the circuit. Solution:...
Read More →Find the value of t/τ for which the current in an LR circuit builds up to
Question: Find the value of $t / T$ for which the current in an LR circuit builds up to (a) $90 \%$, (b) $99 \%$ and (c) $99.9 \%$ of the steady-state value. Solution:...
Read More →The current in a solenoid of 240 turns,
Question: The current in a solenoid of 240 turns, having a length of $12 \mathrm{~cm}$ and a radius of $2 \mathrm{~cm}$, changes at a rate of $0.8 \mathrm{~A} / \mathrm{s}$. Find the emf induced in it. Solution:...
Read More →A magnetic flux of
Question: A magnetic flux of $8 \times 10^{-4}$ weber is linked with each other of a 200 turn coil when there is an electric current of $4 \mathrm{~A}$ in it. Calculate the self-inductance of the coil. Solution:...
Read More →Mark against the correct answer in the following:
Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=\sin \left(x^{x}\right)$ then $\frac{d y}{d x}=?$ A. $x^{x} \cos \left(x^{x}\right)$ B. $x^{x} \cos x^{x}(1+\log x)$ C. $x^{x} \cos x^{x} \log x$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in the following: If $y=(\sin x)^{\log x}$ then $\frac{d y}{d x}=?$ A. $(\log x) \cdot(\sin x)^{(\log x-1)} \cdot \cos x$ B. $(\sin x)^{\log x} \cdot\left\{\frac{x \log x+\log \sin x}{x}\right\}$ C. $(\sin x)^{\log x} \cdot\left\{\frac{(x \log x) \cot x+\log \sin x}{x}\right\}$ D. none of these Solution:...
Read More →An average emf of 20V is induced in an inductor
Question: An average emf of $20 \mathrm{~V}$ is induced in an inductor when the current in it is changed from $2.5 \mathrm{~A}$ in one direction to the same value in the opposite direction in $0.1 \mathrm{~s}$. Find the self-inductance of the inductor. Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $y=(\tan x)^{\cot x}$ then $\frac{d y}{d x}=?$ A. $\cot x \cdot(\tan x)^{\cot x-1} \cdot \sec ^{2} x$ B. $-(\tan x)^{\cot x} \cdot \operatorname{cosec}^{2} x$ C. $(\tan x)^{\cot x} \cdot \operatorname{cosec}^{2} x(1-\log \tan x)$ D. none of these Solution:...
Read More →The current in an ideal, long solenoid is varied at a uniform rate of
Question: The current in an ideal, long solenoid is varied at a uniform rate of $0.01 \mathrm{~A} / \mathrm{s}$. The solenoid has 2000 turns/m and its radius is $6.0 \mathrm{~cm}$. (a) Consider a circle of radius $1.0 \mathrm{~cm}$ inside the solenoid with its axis coinciding with the axis of the solenoid. Write the change in the magnetic flux through this circle in $2.0$ seconds. (b) Find the electric field induced at a point on the circumference of the circle. (c) Find the electric field induc...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in the following: If $y=e^{\sin \sqrt{x}}$ then $\frac{d y}{d x}=?$ C. $\frac{e^{\sin \sqrt{x}}}{2 \sqrt{x}}$ D. none of these Solution:...
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