Question
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.
✓
Answer
$\frac{\text{Q}}{2}=\text{Q}\Big(1-\text{e}^{\frac{-\text{t}}{\text{CR}}}\Big)$
$\Rightarrow\frac{1}{2}=\Big(1-\text{e}^{\frac{-\text{t}}{\text{CR}}}\Big)$
$\Rightarrow\text{e}^{\frac{-\text{t}}{\text{CR}}}=\frac{1}{2}$
$\Rightarrow\frac{\text{t}}{\text{RC}}=\log2\Rightarrow\text{n}=0.69.$
$\Rightarrow\frac{1}{2}=\Big(1-\text{e}^{\frac{-\text{t}}{\text{CR}}}\Big)$
$\Rightarrow\text{e}^{\frac{-\text{t}}{\text{CR}}}=\frac{1}{2}$
$\Rightarrow\frac{\text{t}}{\text{RC}}=\log2\Rightarrow\text{n}=0.69.$
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
Compute the typical de Broglie wavelength of an electron in a metal at 27ºC and compare it with the mean separation between two electrons in a metal which is given to be about 2 × 10–10 m.
A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil is suspended vertically and the normal to the plane of the coil makes an angle of 30º with the direction of a uniform horizontal magnetic field of magnitude 0.80 T. What is the magnitude of torque experienced by the coil?
In a diffraction pattern due to a single slit, how will the angular width of central maximum change, if
a. Orange light is used in place of green light,
b. the screen is moved closer to the slit,
c. the slit width is decreased?
Justify your answer in each case.
a. Orange light is used in place of green light,
b. the screen is moved closer to the slit,
c. the slit width is decreased?
Justify your answer in each case.
A pendulum having a bob of mass m is hanging in a ship sailing along the equator from east to west. When the ship is stationary with respect to water the tension in the string is T0.
→- Find the speed of the ship due to rotation of the earth about its axis.
- Find the difference between T0 and the earth's attraction on the bob.
- If the ship sails at speed v, what is the tension in the string? Angular speed of earth's rotation is $\omega$ and radius of the earth is R.
Explain the effect of electric potential (potential difference) on photoelectric current and derive the definition and formula of stopping potential.
By defining conduction current, explain why Maxwell propounded the idea of displacement current?
Estimate the change in the density of water in ocean at a depth of 400m below the surface. The density of water at the surface = 1030kg/m3 and the bulk modulus of water = 2 × 109N/m2.
a. Write the relationship between mobility and drift velocity in a current carrying conductor.
b. Two aluminium wires have their lengths in the ratio 2 : 3 and radii in the ratio 1 : 3. These are connected in parallel across a battery of emf E and of negligible internal resistance. Find the ratio of drift velocities of the electrons in the two wires.
b. Two aluminium wires have their lengths in the ratio 2 : 3 and radii in the ratio 1 : 3. These are connected in parallel across a battery of emf E and of negligible internal resistance. Find the ratio of drift velocities of the electrons in the two wires.
An ideal battery sends a current of 5A in a resistor. When another resistor of value $10\Omega$ is connected in parallel, the current through the battery is increased to 6A. Find the resistance of the first resistor.
→