$A$ nichrome wire has a resistance of $10\, \Omega$. Find the resistance of another nichrome wire,whose length is three times and area of cross-section four times the first wire.

$V-I$ graphs for two wires $A$ and $B$ are shown in the figure. If both the wires are made of the same material and are of equal thickness,which of the two is of more length? Give justification for your answer.

State Joule's law of heating and write its mathematical form.

Two wires of the same metal have the same length, but cross-sections are in the ratio $3 : 1$. They are joined in series. The resistance of the thicker wire is $10\, \Omega$. The total resistance of the combination 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.

The $SI$ unit of resistivity of the material is $......$