Question

Why is series arrangement not used in domestic circuits?

Answer 1

Hint: When two appliances of resistances are connected in series, the total voltage V is split across the resistors as \[{{V}_{1}}\] and \[{{V}_{2}}\] (their values depending on the value of the respective resistors) and the effective resistance of both the resistors increases to the sum of the resistances.
While these appliances are connected parallel to each other, their voltage V is equal across the resistors and the effective resistance reduces.

Complete step by step solution:
When appliances are connected in series, the damage of one of the appliances can disconnect the whole circuit, which means the circuit would stop conducting current. It will be practically difficult to detect the defect and overloading will be an inevitable factor. The detection of any damage in the circuit wires or loose contact could be done easily if the circuit is connected parallel. Moreover, as the voltage is split according to the value of resistors in series connection, the input voltage to a household will have to be too high. This high voltage supplied to any home can cause heavy damage. Hence connecting appliances with high resistances in series is practically a dangerous application. Though the series connection in homes is less complex to connect, it is avoided to the maximum because of these harmful reasons. Keeping all these factors in mind, household connections are always done parallel with fewer selected ports in series.
Additional information: Here we can find out the effective resistance due to the series arrangement.

In this diagram we can see, three resistors have been connected in series. To check the potential drop we have connected voltmeters through each resistor.
So, the total potential can be written as,
\[\text{V=}{{\text{V}}_{\text{1}}}\text{+}{{\text{V}}_{\text{2}}}\text{+}{{\text{V}}_{\text{3}}}\]
To find the resistance, we can use ohm’s law.
\[{{\text{V}}_{\text{1}}}\text{=I}{{\text{R}}_{\text{1}}}\]
\[{{\text{V}}_{2}}\text{=I}{{\text{R}}_{2}}\]
\[{{\text{V}}_{3}}\text{=I}{{\text{R}}_{3}}\]
We can add these potential drops to find out the total voltage.
\[\text{V=I}{{\text{R}}_{\text{1}}}\text{+I}{{\text{R}}_{\text{2}}}\text{+I}{{\text{R}}_{\text{3}}}\]
\[\text{V=I(}{{\text{R}}_{\text{1}}}\text{+}{{\text{R}}_{\text{2}}}\text{+}{{\text{R}}_{\text{3}}})\]
From this expression, we can say that current will be the same in series circuit.
\[\text{V=IR}\]
i.e. \[\text{R}\] is the equivalent resistance of three resistors.
\[\text{R=}{{\text{R}}_{\text{1}}}\text{+}{{\text{R}}_{\text{2}}}\text{+}{{\text{R}}_{\text{3}}}\]
From this equation, we can conclude that overall resistance increases when the resistors are connected in series.

Note: In parallel connections, the current is split at the junctions. In series connections, voltage is split at the junctions. Load resistors are affixed in all household machines to withstand the standard 220V-240V voltage value.