PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions

A 100 μF capacitor is joined to a 24 V battery through a 1.0 MΩ resistor. Plot qualitative graphs (a) between current and time for the first 10 minutes and (b) between charge and time for the same period.

How many time constants will elapse before the current in a charging RC circuit drops to half of its initial value? Answer the same question for a discharging RC circuit.

How many time constants will elapse before the charge on a capacitors falls to 0.1% of its maximum value in a discharging RC circuit?

How many time constants will elapse before the energy stored in the capacitor reaches half of its equilibrium value in a charging RC circuit?

Two capacitors of capacitances 4⋅0 µF and 6⋅0 µF are connected in series with a battery of 20 V. Find the energy supplied by the battery.

A capacitor of capacitance C is connected to a battery of emf ε at t = 0 through a resistance R. Find the maximum rate at which energy is stored in the capacitor. When does the rate have this maximum value?

A capacitor of capacitance 12.0 μF is connected to a battery of emf 6.00 V and internal resistance 1.00 Ω through resistanceless leads. 12.0 μs after the connections are made, what will be (a) the current in the circuit (b) the power delivered by the battery (c) the power dissipated in heat and (d) the rate at which the energy stored in the capacitor is increasing?

A capacitance C charged to a potential difference V is discharged by connecting its plates through a resistance R. Find the heat dissipated in one time constant after the connections are made. Do this by calculating ∫ i²R dt and also by finding the decrease in the energy stored in the capacitor.

By evaluating ∫i²Rdt, show that when a capacitor is charged by connecting it to a battery through a resistor, the energy dissipated as heat equals the energy stored in the capacitor.

Find the charge on each of the capacitors 0.20 ms after the switch S is closed in the figure.

Each capacitor in figure has a capacitance of 10 µF. The emf of the battery is 100 V. Find the energy stored in each of the four capacitors.

A capacitor with stored energy 4⋅0 J is connected with an identical capacitor with no electric field in between. Find the total energy stored in the two capacitors.

A capacitor of capacitance 100 μF is connected across a battery of emf 6 V through a resistance of 20 kΩ for 4 s. The battery is then replaced by a thick wire. What will be the charge on the capacitor 4 s after the battery is disconnected?

Consider the situation shown in figure. The switch is closed at t = 0 when the capacitors are uncharged. Find the charge on the capacitor C₁ as a function of time t.

A capacitor of capacitance C is given a charge Q. At t = 0, it is connected to an uncharged capacitor of equal capacitance through a resistance R. Find the charge on the second capacitor as a function of time.

A capacitor of capacitance C is given a charge Q. At t = 0, it is connected to an ideal battery of emf ε through a resistance R. Find the charge on the capacitor at time t.

A point charge Q is placed at the origin. Find the electrostatic energy stored outside the sphere of radius R centred at the origin.

A metal sphere of radius R is charged to a potential V.

1. Find the electrostatic energy stored in the electric field within a concentric sphere of radius 2 R.
2. Show that the electrostatic field energy stored outside the sphere of radius 2 R equals that stored within it.

A large conducting plane has a surface charge density `1.0 xx 10^-4  "Cm"^-2` . Find the electrostatic energy stored in a cubical volume of edge 1⋅0 cm in front of the plane.

Figure shows two identical parallel plate capacitors connected to a battery through a switch S. Initially, the switch is closed so that the capacitors are completely charged. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant 3. Find the ratio of the initial total energy stored in the capacitors to the final total energy stored.