Two electric bulbs,rated at $(25\, W, 220\, V)$ and $(100\, W, 220\, V)$,are connected in series across a $220\, V$ voltage source. If the $25\, W$ and $100\, W$ bulbs draw powers $P_1$ and $P_2$ respectively,then

The series combination of two batteries,both of the same emf $10 \; V,$ but different internal resistances of $20 \; \Omega$ and $5 \; \Omega,$ is connected to the parallel combination of two resistors $30 \; \Omega$ and $R \; \Omega.$ If the voltage difference across the battery of internal resistance $20 \; \Omega$ is zero,the value of $R$ (in $\Omega$) is:

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:

$A$ 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 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 $\text{ J/s}$)

$A, B$ and $C$ are voltmeters of resistance $R, 1.5R$ and $3R$ respectively as shown in the figure. When some potential difference is applied between $X$ and $Y$,the voltmeter readings are $V_A, V_B$ and $V_C$ respectively. Then