State $Ohm's$ law. Write the mathematical representation of $Ohm's$ law. Use this relationship to define $1\, ohm.$ List two disadvantages of connecting different electrical appliances in series.

(N/A) $Ohm's$ law: The potential difference across the ends of a resistor is directly proportional to the current flowing through it, provided its temperature remains constant.
Mathematical representation: $V = IR$ or $R = V / I$, where $V$ is the potential difference, $I$ is the current, and $R$ is the resistance.
Definition of $1\, ohm$: If the potential difference across the two ends of a conductor is $1\, V$ and the current flowing through it is $1\, A$, then the resistance $R$ of the conductor is $1\, ohm$ $(1\, \Omega = 1\, V / 1\, A)$.
Disadvantages of series connection:
$(i)$ Different electrical appliances require different values of current to operate properly, which is not possible in a series circuit because the current remains the same throughout.
$(ii)$ If one appliance fails or is switched off, the entire circuit is broken, and none of the other appliances will work.