A capacitance C charged to a potential difference V is discharged… - Vidyadip

Question

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 $\int\text{i}^2\text{R}$ dt and also by finding the decrease in the energy stored in the capacitor.

✓

Answer

Energy stored at a part time in discharging $=\frac{1}{2}\text{CV}^2\Big(\text{e}^{\frac{-\text{t}}{\text{RC}}}\Big)^2$
Heat dissipated at any time = (Energy stored at t = 0) - (Energy stored at time t)
$=\frac{1}{2}\text{CV}^2-\frac{1}{2}\text{CV}^2\big(-\text{e}^{-1}\big)^2$ $=\frac{1}{2}\text{CV}^2\big(1-\text{e}^2\big)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Current Electricity→Current Electricity — all question types→Physics STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

A straight wire of length l can slide on two parallel plastic rails kept in a horizontal plane with a separation d. The coefficient of friction between the wire and the rails is $\mu.$ If the wire carries a current i, what minimum magnetic field should exist in the space in order to slide the wire on the rails?

radioactive isotope has a half-life of 5 years. After how much time is its activity reduced to 3.125% of its original activity?

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

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

Explain the formation of energy band in solids. Draw energy band diagram for (i) a conductor, (ii) an intrinsic semiconductor.

Describe the working of photodiode by drawing the circuit diagram.
Draw the characteristics of a photodiode for different illumination intensities.
Why is photodiode operated in reverse bias even though the reverse bias current is much weaker than the current in forward bias?

Explain the principle and working of a cyclotron with the help of a schematic diagram. Write the expression for cyclotron frequency.

A resistor of $200 \Omega$ and a capacitor of $15.0 \mu F$ are connected in series to a $220 V , 50 Hz$ ac source. (a) Calculate the current in the circuit; (b) Calculate the voltage (rms) across the resistor and the capacitor. Is the algebraic sum of these voltages more than the source voltage? If yes, resolve the paradox.

Two blocks of mares 10kg and 20kg are placed on the X-axis. The first mass is moved on the axis by a distance of 2cm. By what distance should the second mass be moved to keep the position of the centre of mass unchanged?

A hot gas emits radiation of wavelengths 46.0nm, 82.8nm and 103.5nm only. Assume that the atoms have only two excited states and the difference between consecutive energy levels decreases as energy is increased. Taking the energy of the highest energy state to be zero, find the energies of the ground state and the first excited state.

Two heater coils made of same material are connected in parallel across the mains. The length and diameter of the wire of one of coils are double that of the other. Which one of them will produce more heat?