Three identical capacitors are given a charge $Q$ each and they are then allowed to discharge through resistances $R_1, R_2,$ and $R_3$. Their charges,as a function of time,are shown in the graph below. The smallest of the three resistances is

Dimensions of $CR$ are those of

The circuit shown here has two batteries of $8.0 \, V$ and $16.0 \, V$,three resistors of $3 \, \Omega$,$9 \, \Omega$,and $9 \, \Omega$,and a capacitor of $5.0 \, \mu F$. How much is the current $I$ in the circuit in steady state? ................... $A$

$A$ capacitor of capacitance $C$ is charged with the help of a $200 \,V$ battery. It is then discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity $2.5 \times 10^2 \,J/(kg \cdot K)$ and mass $0.1 \,kg$. If the temperature of the block rises by $0.4 \,K$,the value of $C$ is

$A$ capacitor is connected to a $20\, V$ battery through a resistance of $10\, \Omega$. It is found that the potential difference across the capacitor rises to $2\, V$ in $1\, \mu s$. The capacitance of the capacitor is $....\, \mu F$. Given: $\ln(10/9) = 0.105$.

Find the charge in steady state of the capacitor. (in $nC$)