What is meant by "electrical resistance" of a conductor? State how the resistance of a conductor is affected when $(i)$ a low current passes through it for a short duration; $(ii)$ a heavy current passes through it for about $30$ seconds.

$(a)$ 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.

An electric kettle of $2 kW$ works for $2 h$ daily. Calculate the $(a)$ energy consumed in $SI$ and commercial units, and $(b)$ cost of running it in the month of June at the rate of ₹ $3.00$ per unit.

What is the resistance of an ideal ammeter?

Three incandescent bulbs of $100\, W$ each are connected in series in an electric circuit. In another circuit,another set of three bulbs of the same wattage are connected in parallel to the same source. Now,if one bulb in both the circuits gets fused,will the rest of the bulbs continue to glow in each circuit? Give reasons.

$A$ large number of free electrons are present in metals,yet no current flows in the absence of electric potential across it. Explain the statement with reason.