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
The weight of a body at the poles is greater than the weight at the equator. Is it the actual weight or the apparent weight we are talking about? Does your answer depend on whether only the earth's rotation is taken into account or the flattening of the earth at the poles is also taken into account?
A potentiometer wire of length 1 m has a resistance of 10$\Omega$. It is connected to a 6 V battery in series with a resistance of 5$\Omega$. Determine the emf of the primary cell which gives a balance point at 40 cm.
→A block is kept on the floor of an elevator at rest. The elevator starts descending with an acceleration of $12m/s^2.$ Find the displacement of the block during the first 0.2s after the start. Take $g = 10m/s^2.$
→A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is $(\sigma /2ε_0)$ $\hat{\text{n}}$ , where $\hat{\text{n}}$ is the unit vector in the outward normal direction, and σ is the surface charge density near the hole.
→A man has to go 50m due north, 40m due east and 20m due south to reach a field.
- What distance he has to walk to reach the field?
- What is his displacement from his house to the field?
Find the range of frequency of light that is visible to an average human being $(400\text{nm}<\lambda<700\text{nm}).$
→Write the principle of working of a potentiometer. Describe briefly, with the help of a circuit diagram, how a potentiometer is used to determine the internal resistance of a given cell.
An infinitely long thin wire carrying a uniform linear static charge density λ is placed along the z-axis. The wire is set into motion along its length with a uniform velocity $\text{v}=\text{v}\hat{\text{k}}_\text{z}$. Calculate the poynting vector $\text{S}=\frac{1}{\mu_0}(\text{E}\times\text{B})$.
→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.
The inputs A and B are inverted by using two NOT gates and their outputs are fed to the NOR gate as shown below.
Analyse the action of the gates (1) and (2) and identify the logic gate of the complete circuit so obtained. Give its symbol and the truth table.
Analyse the action of the gates (1) and (2) and identify the logic gate of the complete circuit so obtained. Give its symbol and the truth table.