Question
How many time constants will elapse before the power delivered by a battery drops to half of its maximum value in an RC circuit?
✓
Answer
Power $=\text{CV}^2=\text{Q}\times\text{V}$
Now, $\frac{\text{QV}}{2}=\text{QV}\times\text{e}^{\frac{-\text{t}}{\text{RC}}}$
$\Rightarrow\frac{1}{2}=\text{e}^{\frac{-\text{t}}{\text{RC}}}$
$\Rightarrow\frac{\text{t}}{\text{RC}}=-\text{In}\ 0.5$
$\Rightarrow-(-0.69)=0.69.$
Now, $\frac{\text{QV}}{2}=\text{QV}\times\text{e}^{\frac{-\text{t}}{\text{RC}}}$
$\Rightarrow\frac{1}{2}=\text{e}^{\frac{-\text{t}}{\text{RC}}}$
$\Rightarrow\frac{\text{t}}{\text{RC}}=-\text{In}\ 0.5$
$\Rightarrow-(-0.69)=0.69.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
→→→→→→→→→
A free atom of iron emits $\text{K}_\alpha$ X-rays of energy 6.4keV. Calculate the recoil kinetic energy of the atom. Mass of an iron atom = 9.3 × 10-26kg.
→If a charge is placed at rest in an electric field, will its path be along a line of force? Discuss the situation when the lines of force are straight and when they are curved.
Calculate the height of the potential barrier for a head on collision of two deuterons. (Hint: The height of the potential barrier is given by the Coulomb repulsion between the two deuterons when they just touch each other. Assume that they can be taken as hard spheres of radius 2.0 fm.)
Consider the plane S formed by the dipole axis and the axis of earth. Let P be point on the magnetic equator and in S. Let Q be the point of intersection of the geographical and magnetic equators. Obtain the declination and dip angles at P and Q.
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.
The ground state energy of hydrogen atom is – 13.6 eV. If an electron makes a transition from an energy level – 0.85 eV to – 3.4 eV, calculate the wavelength of the spectral line emitted.To which series of hydrogen spectrum does this wave length belong?
A violin player riding on a slow train plays a 440Hz note. Another violin player standing near the track plays the same note. When the two are close by and the train approaches the person on the ground, he hears 4.0 beats per second. The speed of sound in air = 340m/s.
- Calculate the speed of the train.
- What beat frequency is heard by the player in the train?
A magnifying glass is a converging lens placed close to the eye. A farsighted person uses spectacles having converging lenses. Compare the functions of a converging lens used as a magnifying glass and as spectacles.
A semicircular wire has a length L and mass M.A particle of mass m is placed at the centre of the circle. Find the gravitational attraction on the particle due to the wire.