The potential difference across a conductor is doubled,the rate of generation of heat will

$(a)$ Derive the formula for the calculation of work done when current flows through a resistor.
$(b)$ One electric bulb is rated $40 \ W$ and $240 \ V$ and another is $25 \ W$ and $240 \ V$. Which bulb has higher resistance and how many times?

What will happen to the current in a circuit,if its resistance is doubled?

Two students perform experiments on series and parallel combinations of two given resistors $R_{1}$ and $R_{2}$ and plot the following $V-I$ and $I-V$ graphs. Which of the graphs is (are) correctly labelled in terms of the words 'series' and 'parallel'? Justify your answer.

Draw a circuit diagram for a circuit consisting of a battery of five cells of $2 \text{ V}$ each, a $5 \, \Omega$ resistor, a $10 \, \Omega$ resistor, and a $15 \, \Omega$ resistor, an ammeter, and a plug key; all connected in series. Also, connect a voltmeter to record the potential difference across the $15 \, \Omega$ resistor and calculate:
$(i)$ the electric current passing through the above circuit and
$(ii)$ the potential difference across the $5 \, \Omega$ resistor when the key is closed.

There is a frill of $20$ bulbs connected in series in a room. One bulb gets fused. The remaining $19$ are again joined in series and connected to the same supply. Will the light increase or decrease in the room?