State Kirchhoff’s first law in words.
Determine the resistance of the lamp in Fig. 6.1.
Determine the battery’s internal resistance $r$.
The battery initially stores $470\\,\\text{kJ}$ of energy. Assume that the e.m.f. and the current in the battery stay constant with time. Calculate the time taken for the energy stored in the battery to drop to $240\\,\\text{kJ}$.
The filament wire of the lamp is joined in series with the neighbouring copper connecting wire in the circuit, as shown in Fig. 6.3. Table 6.1 gives some data for the filament wire and the neighbouring copper connecting wire. The cross-sectional area of the filament wire is $A$ and that of the copper wire is $360A$. The number density of free electrons in the filament wire is $n$ and that in the copper wire is $2.5n$. Calculate the ratio $$\\frac{\\text{average drift speed of free electrons in filament wire}}{\\text{average drift speed of free electrons in copper wire}}.$$