What is the lowest resistance that can be obtained by combining four coils of resistances $4\, \Omega, 8\, \Omega, 12\, \Omega$ and $24\, \Omega$?

$(a)$ 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.

$(a)$ What do the following symbols represent in a circuit? Write the name and one function of each.
$(b)$ Draw a schematic diagram of a circuit consisting of a battery of $12 \, V$,three resistors of $5 \, \Omega$,$10 \, \Omega$,and $20 \, \Omega$ connected in parallel,an ammeter to measure the total current through the circuit,and a voltmeter to measure the potential difference across the combination of resistors.
$(c)$ State any one advantage of connecting electrical devices in parallel with the mains instead of connecting them in series in a household circuit.

In the following circuits (Figure),heat produced in the resistor or combination of resistors connected to a $12\, V$ battery will be

$1 \; kWh = \ldots \ldots \ldots \; \text{watt-seconds}$

Define $1$ volt.