$A$ battery of emf $12 \text{ V}$ and internal resistance $4 \Omega$ is connected to a resistor. If the current in the circuit is $0.8 \text{ A}$,then the resistance of the resistor is: (in $Omega$)

Four identical electrical lamps are labelled $1.5\,V$,$0.5\,A$,which describes the condition necessary for them to operate at normal brightness. $A$ $12\,V$ battery of negligible internal resistance is connected to the lamps as shown. Then:

In the given circuit,the value of $\left|\frac{I_1+I_3}{I_2}\right|$ is

The charge flowing through a resistance $R$ varies with time $t$ as $Q = at - bt^2$,where $a$ and $b$ are positive constants. The total heat produced in $R$ is

Find the equivalent resistance between $A$ and $B$.

What is the maximum number of $50 \, W - 100 \, V$ bulbs that can be connected in parallel to a battery of $120 \, V$ and $10 \, \Omega$ internal resistance so that they glow with maximum intensity?