$A$ hot plate of an electric oven connected to a $220\, V$ line has two resistance coils $A$ and $B$,each of $24\,\Omega$ resistance,which may be used separately,in series,or in parallel. What are the currents in the three cases?

$(a)$ Calculate the resistance of the wire using the graph.
$(b)$ How many $176 \,\Omega$ resistors in parallel are required to carry $5\, A$ on a $220\, V$ line?
$(c)$ Define electric power. Derive the relation between power,potential difference,and resistance.

$A$ cell,a resistor,a key and an ammeter are arranged as shown in the circuit diagrams of the figure. The current recorded in the ammeter will be

Draw a circuit diagram for a circuit consisting of a battery of five cells of $2 \text{ V}$ each, a $5 \, \Omega$ resistor, a $10 \, \Omega$ resistor, and a $15 \, \Omega$ resistor, an ammeter, and a plug key; all connected in series. Also, connect a voltmeter to record the potential difference across the $15 \, \Omega$ resistor and calculate:
$(i)$ the electric current passing through the above circuit and
$(ii)$ the potential difference across the $5 \, \Omega$ resistor when the key is closed.

Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combinations would be -

The table given below provides the resistivity of three samples in $\Omega \cdot m$:

Sample	Resistivity $(\Omega \cdot m)$
$A$	$1.6 \times 10^{-8}$
$B$	$7.5 \times 10^{17}$
$C$	$44 \times 10^{-6}$

$(a)$ Which of them is a good conductor? Which is an insulator? Why?
$(b)$ $A$ wire of resistance $4 \ \Omega$ is folded on itself to double its thickness. Calculate the new resistance of the wire.