Which has a greater resistance$-$a $100$ $W$ bulb or a $60$ $W$ bulb?

$(a)$ $(i)$ What is meant by saying that the potential difference between two points is $1 \, V$? $(ii)$ How much energy is given to $5 \, C$ of charge passing through a $12 \, V$ battery? $(b)$ Describe an activity with a necessary electric circuit to study the factors on which the resistance of a conducting wire depends.

The potential difference across the terminals of a cell is $1.5 \ V$. If it is connected with a resistance of $30 \ \Omega$,calculate the current flowing through the circuit. (in $A$)

$(a)$ 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?

$A$ cylindrical conductor of length $l$ and uniform area of cross-section $A$ has resistance $R$. Another conductor of length $2l$ and resistance $R$ of the same material has area of cross-section:

Derive the relation $R = R_{1} + R_{2} + R_{3}$ when three resistors $R_{1}, R_{2}$ and $R_{3}$ are connected in series in an electric circuit.