For the circuit shown in figure, find

(i) the initial current through each resistor

(ii) steady state current through each resistor

(iii) final energy stored in the capacitor

(iv) time constant of the circuit when switch is closed.

(v) time constant of the circuit when switch is open

In the network shown in figure, find $I,I_1$ and the charge on the $7\mathrm{\mu F}$ capacitor after steady state condition is reached.

A leaky parallel plate capacitor is filled completely with a material having dielectric constant K = 5 and electrical conductivity $\sigma =7.4\times {10}^{-12}{\Omega }^{-1}{m}^{-1}.$ If the charge on the capacitor at the instant t = 0 is $q_0=8.55\mu C$, then calculate the leakage current at the instant t = 12 s.

In the circuit shown in figure, all wires have equal resistance $r$. Find the equivalent resistance between $A$ and $B$.

A hemisphere network of radius '$a$' is made by using a conducting wire of resistance per unit length $r$. Find the equivalent resistance across $OP$.

A total charge $Q$ flows across a resistor $R$ during a time interval $T$ in such a way that the current $v/s$ time graph for $0\to T$ is like the loop of a sin curve in the range $0\to \pi$. What will be the total heat generated in the resistor.