In the given circuit, determine current through branch having indicated resistor $R_4$. Given $R_1=R_2=4\mathrm{\Omega },\mathrm{}{R}_3=R_4=R_5=2\mathrm{\Omega },{\mathrm{\epsilon }}_1=5\mathrm{V},\mathrm{}{\mathrm{\epsilon }}_2=10\mathrm{V}$

Determine current through batteries ${\epsilon }_1$, and ${\epsilon }_2$.

Find the equivalent resistance across terminals $P$ and $Q$ as shown in figure. Each resistance in circuit is $R$.

Consider the circuit shown in figure. If the switch is closed at $t=0$, then calculate the values of $I\text{,} I_1$ and $I_2$ at,

$$ $\left(a\right) t=0$, $\left(b\right)$ $t=\infty$

The figure shows three sections of the circuit that are to be connected in turn to the same battery via a switch. The resistors are all identical as are capacitors. Rank the sections according to,

(A) the final (equilibrium) charge on the capacitor.

(B) the time required for the capacitor to reach $50\mathrm{\%}$ of its final charge, greatest first.

Determine the current through the battery in the circuit shown in figure.

(A) immediately after the switch $S$ is closed

(B) after a long time.

A varying voltage is applied to the clamps $AB$ as shown in figure such that the voltage across the capacitor plates varies as shown in the figure. Plot the time depending on voltage across the clamps $CD$.

Consider the network shown in figure. Initially, the switch $S_1$ is closed and $S_2$ is open.

(A) Calculate $V_{\mathrm{A}}-V_{\mathrm{B}}$.

(B) When $S_2$ is also closed, what is $V_{\mathrm{A}}-V_{\mathrm{B}}$,

(i) just after closing, (ii) after a long time.

In the circuit shown in the figure, $R_1=10 \mathrm{\Omega }, R_2=20 \mathrm{\Omega }, C_1=\mathrm{\mu }\mathrm{F},C_2=2 \mathrm{\mu }\mathrm{F}$, and $E=6 \mathrm{V}$. Calculate the charge on each capacitor in the steady-state.