eSaral - JEE | NEET | Class 8-10 Exam Prep App

A parallel-plate capacitor has plate area

Question: A parallel-plate capacitor has plate area $40 \mathrm{~cm}^{2}$ and separation between the plates $0.10 \mathrm{~mm}$ is connected to a battery of emf $2.0 \mathrm{~V}$ through a $16 \Omega$ resistor. Find the electric field in the capacitor $10 \mathrm{~ns}$ after the connections are made. Solution:...

A capacitor of capacitance 10 μF is connected to

Question: A capacitor of capacitance $10 \mu \mathrm{F}$ is connected to a battery of emf $2 \mathrm{~V}$. It is found that it takes $50 \mathrm{~ms}$ for the charge on the capacitor to become $12.6 \mu \mathrm{C}$. Find the resistance of the circuit. Solution:...

A parallel-plate capacitor with plate area

Question: A parallel-plate capacitor with plate area $20 \mathrm{~cm}^{2}$ and plate separation $12.0 \mathrm{~mm}$ is connected to a battery. The resistance of the circuit is $10 \mathrm{k} \Omega$. Find the time constant of the circuit. Solution:...

A capacitance C, a resistance R and

Question: A capacitance $C$, a resistance $R$ and an emf $\varepsilon$ are connected in series at $t=0$. What is the maximum value of, (a) The potential difference across the resistor, (b) The current in the circuit, (c) The potential difference across the capacitor, (d) The energy stored in the capacitor, (e) The power delivered by the battery and (f) The power converted into heat. Solution:...

Using differentials, find the approximate values of:

Question: Using differentials, find the approximate values of: find the approximate values of $\sqrt{37}$. Solution:...

Find the potential difference between the points A and B

Question: Find the potential difference between the points $A$ and $B$ and between the points $B$ and $C$ of figure (32-E33) in steady state. Solution:...

Find the chargers on the four capacitors of capacitances 1 μF, 2 μF, 3 μF

Question: Find the chargers on the four capacitors of capacitances $1 \mu \mathrm{F}, 2 \mu \mathrm{F}, 3 \mu \mathrm{F}$ and $4 \mu \mathrm{F}$ shown in figure (32-E32). Solution:...

The sides of an equilateral triangle are increasing at the rate of

Question: The sides of an equilateral triangle are increasing at the rate of $2 \mathrm{~cm} / \mathrm{sec}$. Find the rate at which the area is increasing when the side is $10 \mathrm{~cm}$. Solution:...

Find the current in the 20Ω resistor shown in figure (32-E31).

Question: Find the current in the $20 \Omega$ resistor shown in figure (32-E31). If a capacitor of capacitance $4 \mu \mathrm{F}$ is joined between the points A and B, what would be the electrostatic energy stored in it in steady state. Solution:...

An edge of a variable cube is increasing at the rate of

Question: An edge of a variable cube is increasing at the rate of $5 \mathrm{~cm} / \mathrm{s}$. How fast is the volume of the cube increasing when the edge is $10 \mathrm{~cm}$ long? Solution:...

Find the charge on the capacitor shown in figure (32-E30).

Question: Find the charge on the capacitor shown in figure (32-E30). Solution:...

Consider the potentiometer circuit arranged as in figure (32-E29).

Question: Consider the potentiometer circuit arranged as in figure (32-E29). The potentiometer wire is $600 \mathrm{~cm}$ long. (a) At what distance from the point A should the jockey touch the wire to get zero deflection in the galvanometer? (b) If the jockey touches the wire at a distance of $560 \mathrm{~cm}$ from A, what will be the current in the galvanometer? Solution:...

A 6 volt battery of negligible internal resistance is connected across a uniform

Question: A 6 volt battery of negligible internal resistance is connected across a uniform wire AB of length $100 \mathrm{~cm}$. The positive terminal of another battery of emf $4 \mathrm{~V}$ and internal resistance $1 \Omega$ is joined to the point A as shown in the figure (32-E28). Take the potential at $B$ to be zero. (a) What are the potentials at the points $A$ and $C$ ? (b) At which point $D$ of the wire $A B$, the potential is equal to the potential at $C$ ? (c) If the points $C$ and $D$...

The radius of a balloon is increasing at the rate of

Question: The radius of a balloon is increasing at the rate of $10 \mathrm{~m} / \mathrm{s}$. At what rate is the surface area of the balloon increasing when the radius is $15 \mathrm{~cm}$ ? Solution:...

The potentiometer wire AB shown in figure (32-E27)

Question: The potentiometer wire $A B$ shown in figure (32-E27) is $50 \mathrm{~cm}$ long. When $A D=30 \mathrm{~cm}$, no deflection occurs in the galvanometer. Find R. Solution:...

Find an angle x which increases twice as fast as its sine.

Question: Find an angle $x$ which increases twice as fast as its sine. Solution:...

A capacitor of capacitance 8.0 μF

Question: A capacitor of capacitance $8.0 \mu \mathrm{F}$ is connected to a battery of emf $6.0 \mathrm{~V}$ through a resistance of $24 \Omega$. Find the current in the circuit (a) Just after the connections are made and (b) One time constant after the connections are made Solution:...

The plates of a capacitor of capacitance 10μF,

Question: The plates of a capacitor of capacitance $10 \mu \mathrm{F}$, charged to $60 \mu \mathrm{C}$, are joined together by a wire of resistance $10 \Omega$ at $t=0$. Find the charge on the capacitor in the circuit at (a) $t=0$, (b) $t=30 \mu \mathrm{s}$, (c) $t=120 \mu \mathrm{s}$ and (d) $t=1.0 \mathrm{~ms}$ Solution:...

A man is moving away from

Question: A man is moving away from a $40-\mathrm{m}$ high tower at a speed of $2 \mathrm{~m} / \mathrm{s}$. Find the rate is which the angle of elevation of the top of the tower is changing when he is at a distance of 30 metres from the foot of the tower. Assume that the eye level of the man is $1.6 \mathrm{~m}$ from the ground. Solution:...

A 13-m long ladder is leaning against a wall. The bottom of the ladder is pulled along the ground, away from

Question: A 13-m long ladder is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of $2 \mathrm{~m} / \mathrm{s}$. How fast is its height on the wall decreasing when the foot of the ladder is $5 \mathrm{~m}$ away from the wall? Solution:...

Solve this following

Question: Oil is leaking at the rate of $15 \mathrm{~mL} / \mathrm{s}$ from a vertically kept cylindrical drum containing oil. If the radius of the drum is $7 \mathrm{~cm}$ and its height is $60 \mathrm{~cm}$, find the rate at which the level of the oil is changing when the oil level is $18 \mathrm{~cm}$. Solution:...

Water is dripping through a tiny hole at the vertex in the bottom of a conical funnel at a uniform rate of 4

Question: Water is dripping through a tiny hole at the vertex in the bottom of a conical funnel at a uniform rate of 4 $\mathrm{cm}^{3} / \mathrm{s}$. When the slant height of the water is $3 \mathrm{~cm}$, find the rate of decrease of the slant height of the water, given that the vertical angle of the funnel is $120^{\circ}$. Solution:...

At 20 μF capacitor is joined to a battery of

Question: At $20 \mu \mathrm{F}$ capacitor is joined to a battery of emf $6.0 \mathrm{~V}$ through a resistance of $100 \Omega$. Find the charge on the capacitor $2.0$ ms after the connections are made. Solution:...

The potentiometer wire AB shown in figure (32-E26) is 40cm long.

Question: The potentiometer wire AB shown in figure (32-E26) is $40 \mathrm{~cm}$ long. Where the free end of the galvanometer should be connected on $\mathrm{AB}$ so that the galvanometer may show zero deflection? Solution:...

Sand is pouring from a pipe at the rate of

Question: Sand is pouring from a pipe at the rate of $18 \mathrm{~cm}^{3} / \mathrm{s} .$ The falling sand forms a cone on the ground in such a way that the height of the cone is one-sixth of the radius of the base. How fast is the height of the sand cone increasing when its height is $3 \mathrm{~cm}$ ? Solution:...

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