Download App

Electric Current in Conductors — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsElectric Current in Conductors3 Marks
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

Physics STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

An ac genrator is made from area of cross section $3 m^2$ and a coil of 100 turns which is rotated by a constant angular velocity of $60 rad / s$ in a magnetic field of 0.04 T . Resistance of the coil is $500 \Omega$ Calculate: (i) maxumum current obtained from the generator and (ii) maximum power dissipated in the coil.
→
The drift current in a reverse-biased p-n junction increases in magnitude if the temperatu,re of the junction is increased. Explain this on the basis of creation of hole-electron pairs.
→
A uniform conducting wire of length 12a and resistance R is wound up as a current carrying coil in the shape of:
  1. An equilateral triangle of side a.
  2. A square of sides a.
  3. A regular hexagon of sides a. The coil is connected to a voltage source $V_0.$ Find the magnetic moment of the coils in each case.
→
Two particles of masses $m_1$ and $m_2$ are joined by a light rigid rod of length r. The system rotates at an angular speed co about an axis through the centre of mass of the system and perpendicular to the rod. Show that the angular momentum of the system is $\text{L}=\mu\text{r}^2\omega$ where $\mu$ is the reduced mass of the system defined as $\mu=\frac{\text{m}_1\text{m}_2}{\text{m}_1+\text{m}_2}.$
→
A point charge is moving along a straight line with a constant velocity u. Consider a small area A perpendicular to the direction of motion of the charge (El). Calculate the displacement current through the area when its distance from the charge is x. The value of x is not large so that the electric field at any instant is essentially given by Coulomb's law.
→
Explain : Bar magnet as an equivalent solenoid.
→
Establish an expression for mobility by giving definition of mobility. Establish relation between mobility of free electrons and electric current.
→
A cell of emf E and internal resistance r is connected across an external resistance R. Plot a graph showing the variation of P.D. across R, verses R.
→
A long charged cylinder of linear charge density $+\lambda_1$ is surrounded by a hollow coaxial conducting cylinder of linear charge density $-\lambda_2$. Use Gauss’s law to obtain expressions for the electric field at a point (i) in the space between the cylinders, and (ii) outside the larger cylinder.
→
A spherical shell made of plastic, contains a charge Q distributed uniformly over its surface. What is the electric field inside the shell? If the shell is hammered to deshape it without altering the charge, will the field inside be changed? What happens if the shell is made of a metal?
→