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Question: If $x=a(\theta-\sin \theta), y=a(1-\cos \theta)$, find $\frac{d y}{d x}$ at $\theta=\frac{\pi}{2}$ Solution:...
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Question: If $x=\frac{1+\log t}{t^{2}}$ and $y=\frac{3+2 \log t}{t} \frac{d y}{d x}=t$ Solution:...
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Question: If $x=2 \cos t-2 \cos ^{3} t, y=\sin t-2 \sin ^{3} t$, show that $\frac{d y}{d x}=\cot t$ Solution:...
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Question: Find $\frac{d y}{d x}$, when $x=\cos ^{-1} \frac{1}{\sqrt{1+t^{2}}}, y=\sin ^{-1} \frac{t}{\sqrt{1+t^{2}}}$ Solution:...
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Question: Find $\frac{d y}{d x}$, when $x=\frac{1-t^{2}}{1+t^{2}}, y=\frac{2 t}{1+t^{2}}$ Solution:...
Read More →Find the value of i1/i2 in figure (32-E3) if (a) R=0.1Ω (b)R=1Ω (c) R=10Ω.
Question: Find the value of $\mathrm{i}_{1} / \mathrm{i}_{2}$ in figure (32-E3) if (a) $\mathrm{R}=0.1 \Omega$ (b) $\mathrm{R}=1 \Omega$ (c) $\mathrm{R}=10 \Omega$. Note from your answers that in order to get more current from a combination of two batteries they should be joined in parallel if the external resistance is small and in series if the external resistance is large as compared to the internal resistances. Solution:...
Read More →The internal resistance of an accumulator battery of
Question: The internal resistance of an accumulator battery of emf $6 \mathrm{~V}$ is $10 \Omega$ when it is fully discharged. As the battery gets charged up, its internal resistance decreases to $1 \Omega$. The battery in its completely discharged state is connected to a charger which maintains a constant potential difference of $9 \mathrm{~V}$. find the current through the battery. (a)Just after the connections are made and (b) After a long time when it is completely charged. Solution:...
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Question: Find $\frac{d y}{d x}$, when $x=\frac{3 a t}{\left(1+t^{2}\right)}, y=\frac{3 a t^{2}}{\left(1+t^{2}\right)}$ Solution:...
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Question: Find $\frac{d y}{d x}$, when $x=a(\cos \theta+\theta \sin \theta), y=a(\sin \theta-\theta \cos \theta)$ Solution: $=\tan \theta$ ANS...
Read More →The potential difference between the terminals of
Question: The potential difference between the terminals of a $6.0 \mathrm{~V}$ battery is $7.2 \mathrm{~V}$ when it is being charged by a current of $2.0 \mathrm{~A}$. What is the internal resistance of the battery? Solution:...
Read More →The potential difference between the terminals of a battery of
Question: The potential difference between the terminals of a battery of emf $6.0 \mathrm{~V}$ and internal resistance $1 \Omega$ drops to $5.8 \mathrm{~V}$ when connected across an external resistor. Find the resistance of an external resistor. Solution:...
Read More →Figure (32-E2) shows an arrangement to measure the
Question: Figure (32-E2) shows an arrangement to measure the emf $\varepsilon$ and internal resistance r of battery. The voltmeter has a very high resistance and ammeter also has some resistance. The voltmeter reads $1.52 \mathrm{~V}$ when the switch $\mathrm{S}$ is open. When the switch is closed the voltmeter reading drops to $1.45 \mathrm{~V}$ and ammeter reads $1.0 \mathrm{~A}$. find the emf and internal resistance of the battery. Solution:...
Read More →The current in a conductor and the potential difference across
Question: The current in a conductor and the potential difference across its ends are measured by an ammeter and a voltmeter. The meters draw negligible currents. The ammeter is accurate but the voltmeter has a zero error (that is, it doesn't read zero when no potential difference is applied). Calculate the zero error if the readings for two different conditions are $1.75 \mathrm{~A}, 14.4$ $\mathrm{V}$ and $2.75 \mathrm{~A}, 22.4 \mathrm{~V}$ Solution:...
Read More →The resistances of an iron wire and a copper wire at
Question: The resistances of an iron wire and a copper wire at $20^{\circ} \mathrm{C}$ are $3.9 \Omega$ and $4.1 \Omega$ respectively. At what temperature will the resistances be equal? Temperature coefficient of resistivity for iron is $5.0 \times 10^{-3} \mathrm{~K}^{-1}$ and for copper it is $4.0 \times 10^{-3} \mathrm{~K}^{-1}$. Neglect any thermal expansion. Solution:...
Read More →A wire has a length of 2.0m and a resistance of 5.0Ω.
Question: A wire has a length of $2.0 \mathrm{~m}$ and a resistance of $5.0 \Omega$. Find the electric field existing inside the wire if it carries a current of 10A. Solution:...
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Question: Find $\frac{d y}{d x}$, when $x=\sqrt{\sin 2 \theta}, y=\sqrt{\cos 2 \theta}$ Solution:...
Read More →Calculate the electric field in a copper wire of cross-sectional
Question: Calculate the electric field in a copper wire of cross-sectional area $2.0 \mathrm{~mm}^{2}$ carrying a current of $1 \mathrm{~A}$. The resistivity of copper $=1.7 \times 10^{-8} \Omega-\mathrm{m}$. Solution:...
Read More →A copper wire of radius 0.1mm and resistance 1kΩ
Question: A copper wire of radius $0.1 \mathrm{~mm}$ and resistance $1 \mathrm{k} \Omega$ is connected across a power supply of $20 \mathrm{~V}$. (a) How many electrons are transferred per second between the supply and the wire at one end? (b) Write down the current density in the wire. Solution:...
Read More →Figure (32-E1) shows a conductor of length I having a circular cross-section.
Question: Figure (32-E1) shows a conductor of length I having a circular cross-section. The radius of cross-section varies linearly from a to $b$. the resistivity of the material is $\rho$. Assuming that $b-a$, find the resistance of the conductor. Solution:...
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Question: Find $\frac{d y}{d x}$, when $x=\cos \theta+\cos 2 \theta, y=\sin \theta+\sin 2 \theta$ Solution:...
Read More →What length of a copper wire of cross-sectional area
Question: What length of a copper wire of cross-sectional area $0.01 \mathrm{~mm}^{2}$ will be needed to prepare a resistance of $1 \mathrm{k} \Omega$ ? Resistivity of copper $=1.7 \times 10^{-8} \Omega-\mathrm{m}$. Solution:...
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Question: Find $\frac{d y}{d x}$, when $x=(\log t+\cos t), y=\left(e^{t}+\sin t\right)$ Solution:...
Read More →Consider a wire of length 4m and cross-sectional area
Question: Consider a wire of length $4 \mathrm{~m}$ and cross-sectional area $1 \mathrm{~mm}^{2}$ carrying a current of $2 \mathrm{~A}$. If each cubic meter of the material contains $10^{29}$ free electrons, find the average time taken by an electron to cross the length of the wire. Solution:...
Read More →A uniform wire of resistance 100Ω is melted and recast
Question: A uniform wire of resistance $100 \Omega$ is melted and recast in a wire of length double that of the original. What would be the resistance of the wire? Solution:...
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Question: Find $\frac{d y}{d x}$, when $x=a \log t, y=b \sin t$ Solution:...
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