$(a)$ Three resistors $R_{1}, R_{2}$ and $R_{3}$ are connected in parallel and the combination is connected to a battery,ammeter,voltmeter,and key. Draw a suitable circuit diagram. Obtain an expression for the effective resistance of the combination of resistors in parallel.
$(b)$ Why are electric bulbs filled with chemically inactive nitrogen or argon?
$(c)$ What is meant by the statement that the rating of a fuse in a circuit is $5 \ A$?

(N/A) The circuit diagram shows three resistors $R_{1}, R_{2}, R_{3}$ connected in parallel across a potential difference $V$. The total current $I$ splits into $I_{1}, I_{2}, I_{3}$ through the resistors.
Since they are in parallel,the potential difference $V$ across each resistor is the same.
Total current $I = I_{1} + I_{2} + I_{3}$.
Using Ohm's law,$I_{1} = V/R_{1}$,$I_{2} = V/R_{2}$,and $I_{3} = V/R_{3}$.
If $R_{p}$ is the equivalent resistance,$I = V/R_{p}$.
Substituting these,$V/R_{p} = V/R_{1} + V/R_{2} + V/R_{3}$.
Thus,$1/R_{p} = 1/R_{1} + 1/R_{2} + 1/R_{3}$.
$(b)$ Electric bulbs are filled with chemically inactive gases like nitrogen or argon to prevent the oxidation of the tungsten filament at high temperatures,thereby prolonging its life.
$(c)$ The statement means that the fuse is designed to allow a maximum current of $5 \ A$ to flow through the circuit. If the current exceeds this value,the fuse wire melts due to excessive heating and breaks the circuit,protecting the appliances.