Find the final charges in steady state on the four capacitors of capacitance $2\mathrm{\mu F}, 4\mathrm{\mu F}, 6\mathrm{\mu F} \mathrm{and} 8\mathrm{\mu F}$ as shown in figure. (Assuming initially they are uncharged). Also find the current through the wire $\mathrm{AB}$ at steady state.

 

A capacitor is connected to a $12 \mathrm{V}$ battery through a resistance of $10\mathrm{\Omega }$. It is found that the potential difference across the capacitor rises to $4.0 \mathrm{V}$ in $1\mathrm{\mu s}.$Find the capacitance of the capacitor.

(Given : $\ln 3 = 1.0986$, $\ln 2 = 0.693$)

A capacitor of capacity $1\mathrm{\mu F}$ is connected in a closed series circuit with a resistance of ${10}^7 \mathrm{ohms}$, an open key and a cell of $2 \mathrm{V}$ with negligible internal resistance:

$\left(\mathrm{i}\right)$ When the key is switched on at time$\mathrm{t} = 0$, find;

$\left(\mathrm{a}\right)$ The time constant for the circuit.

$\left(\mathrm{b}\right)$ The charge on the capacitor at steady state.

$\left(\mathrm{c}\right)$ Time taken to deposit charge equal to half of charge that will deposit at steady state.

$\left(\mathrm{ii}\right)$ If after completely charging the capacitor, the cell is shorted by zero resistance at time $\mathrm{t} = 0,$ find the charge on the capacitor at $\mathrm{t} = 50 \mathrm{s}.$ $(\mathrm{Given} : {\mathrm{e}}^{–5} = 6.73\times {10}^{–3} , l\mathrm{n}2 = 0.693)$

A $5.0 \mathrm{\mu } \mathrm{F}$ capacitor having a charge of $20 \mathrm{\mu } \mathrm{C}$ is discharged through a wire of resistance $5.0 \mathrm{\Omega }$. Find the heat dissipated in the wire between $25 \mathrm{to} 50 \mu \mathrm{s}$after the connections are made. (Given :${\mathrm{e}}^{–2} = 0.135$)

A varying voltage is applied to the clamps $\mathrm{AB}$ (figure a) such that the voltage across the capacitor plates varies as shown in figure b.

Plot the time dependence of voltage across the clamps $\mathrm{CD}$.

A capacitor of capacitance $\mathrm{C}$ is charged by charge ${\mathrm{q}}_0.$ At $\mathrm{t} = 0,$ it is connected to a battery of emf V and internal resistance $\mathrm{r}$. Find the charge on the capacitor at time $\mathrm{t}$ (positive plate of capacitor connected with positive plate of battery).

In the circuit shown find

$\left(\mathrm{a}\right)$ the power drawn from the cell,

$\left(\mathrm{b}\right)$ the power consumed by the resistor which is converted into heat and

$\left(\mathrm{c}\right)$ the power given to the inductor.

A current of $5 \mathrm{A}$ exists in a $10 \mathrm{\Omega }$ resistance for $4 \mathrm{minutes}$.

$\left(\mathrm{i}\right)$ How many coulombs and

$\left(\mathrm{ii}\right)$ How many electrons pass through any cross-section of the resistor at this time? Charge of the $\mathrm{electron}=1.6\times {10}^{-19} \mathrm{C}$.