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 potential difference across the $8\ \Omega$ resistance is $48\ V$ as shown in the figure. The value of the potential difference across points $X$ and $Y$ will be ............... $V$.

The charge supplied by a source varies with time $t$ as $Q = at - bt^2$. Find the total heat produced in the $2R$ resistor before the current reduces to zero.

$A$ student connects a voltmeter,ammeter,and resistance according to the circuit given. If the voltmeter reading is $20\, V$ and the ammeter reading is $4\, A$,then the resistance $R$ will be:

In the circuit shown, if the current through the resistor $R$ is $\frac{1}{5} \, A$, the value of $R$ is (in $\Omega$)

One end of a Nichrome wire of length $2L$ and cross-sectional area $A$ is attached to an end of another Nichrome wire of length $L$ and cross-sectional area $2A$. If the free end of the longer wire is at an electric potential of $8.0\,V$,and the free end of the shorter wire is at an electric potential of $1.0\,V$,the potential at the junction of the two wires is equal to ............. $V$.