$A$ car has a fresh battery of $e.m.f.$ $12\, V$ and internal resistance of $0.05\, \Omega$. If the starter motor draws a current of $90\, A$,the terminal voltage when the starter is on will be ............... $V$.

In the circuit shown,the resistance $r$ is a variable resistance. If for $r = fR$,the heat generation in $r$ is maximum,then the value of $f$ is:

$A$ set of $n$ equal resistors,each of value $R$,are connected in series to a battery of emf $E$ and internal resistance $R$. The current drawn is $I$. Now,the $n$ resistors are connected in parallel to the same battery. The current drawn from the battery becomes $10I$. The value of $n$ is:

In the circuit shown, the heat produced in $5 \Omega$ resistance due to current $I_2$ is $50 \text{ J/s}$. Then, the heat generated per second in $2 \Omega$ resistance is (in $\text{ J/s}$)

Given below are two statements:
Statement $I:$ The equivalent resistance of resistors in a series combination is smaller than the least resistance used in the combination.
Statement $II:$ The resistivity of the material is independent of temperature.
In the light of the above statements,choose the correct answer from the options given below:

Six resistors of $3 \; \Omega$ each are connected along the sides of a hexagon and three resistors of $6 \; \Omega$ each are connected along $AC$, $AD$, and $AE$ as shown in the figure. The equivalent resistance between $A$ and $B$ is equal to