The electric current flowing through any conductor is directly proportional to the electric potential difference across the conductor. Which law is this?

$A$ potential difference $V$ is applied across a conductor of length $L$ and diameter $D$. How is the resistance $R$ of the conductor affected,when in turn $(i)$ $V$ is halved,$(ii)$ $L$ is halved,and $(iii)$ $D$ is doubled? Justify your answer in each case.

What is the commercial unit of electrical energy? Represent it in terms of joules.

If a current of $0.5\;A$ is passed through an electric bulb for $1\;hour$, how much electric charge will pass through the bulb (in $C$)?

How are electrical appliances connected to the main line in our homes?

$(a)$ Derive an expression to find the equivalent resistance of three resistors connected in series. Also,draw the schematic diagram of the circuit.
$(b)$ Find the equivalent resistance of the following circuit.