$A$ battery of internal resistance $4\,\Omega$ is connected to a network of resistors as shown in the figure. If maximum power is to be delivered to the network,the magnitude of $R$ in $\Omega$ should be:

Find the current passing through the battery immediately after the key $(K)$ is closed. It is given that initially all the capacitors are uncharged. (Given that $E = 5 \, V$, $R = 6 \, \Omega$) (in $A$)

Two electric bulbs whose resistances are in the ratio of $1 : 2$ are connected in parallel to a constant voltage source. The powers dissipated in them have the ratio:

$P$ and $Q$ are two identical wires of resistance $2000\, \Omega$ each, and $M$ is the midpoint of $PQ$. A voltmeter of resistance $1000\, \Omega$ is connected between $P$ and $M$. When a potential difference of $150\, V$ is applied across $PQ$, the reading of the voltmeter will be ............. $V$.

Twelve wires of equal length and equal cross-sectional area form a cube. If the resistance of each wire is $R$,then the effective resistance between the two ends of a diagonal is:

$A$ storage battery of $emf$ $8.0\; V$ and internal resistance $0.5\; \Omega$ is being charged by a $120\; V$ $DC$ supply using a series resistor of $15.5\; \Omega$. What is the terminal voltage of the battery during charging? What is the purpose of having a series resistor in the charging circuit?