The resistance of the bulb is given by \(R = \frac{V^2}{P} = \frac{200^2}{100} = 400 \, \Omega\). When connected to a \(160 \text{ V}\) supply, the power consumed is \(P' = \frac{V'^2}{R} = \frac{160^2}{400} = 64 \text{ W}\).

Energy is calculated as \( E = P \times t = 100 \, \text{W} \times 10 \, \text{h} = 1000 \, \text{Wh} = 1 \, \text{kWh} \). In standard SI units, this is \( 1000 \, \text{W} \times 3600 \, \text{s} = 3.6 \times 10^6 \, \text{J} \). Thus, both Options (1) and (2) are correct.

Concept: Resistance of metals increases with temperature. Power \(P = V^2/R\).
Formula: \(P = V^2/R\), \(R \propto T\).
Solution: As filament warms, its resistance \(R\) increases. For constant voltage \(V\), current \(I = V/R\) decreases, so power \(P = V^2/R\) delivered to the bulb also decreases. Thus, A and R are true and R explains A.

Concept: Maximum power transfer theorem for cells.
Formula: For a source with EMF \(E_{eq}\) and internal resistance \(r_{eq}\), maximum power is transferred when load \(R_L = r_{eq}\), and \(P_{max} = \frac{E_{eq}^2}{4r_{eq}}\).
Solution: For 2 cells in series: \(E_{eq} = 2E\), \(r_{eq} = 2r\). \(P_{max, series} = \frac{(2E)^2}{4(2r)} = \frac{E^2}{2r}\). Load \(R_L = 2r\).
For 2 cells in parallel: \(E_{eq} = E\), \(r_{eq} = r/2\). \(P_{max, parallel} = \frac{E^2}{4(r/2)} = \frac{E^2}{2r}\). Thus, maximum power transferred is same, so A is true. Load resistances for max power transfer are different, so R is false.

Initially, the bulb's cold filament has lower resistance. As it heats up, resistance increases, causing current to drop (for a constant voltage source). Since power \(P = V^2/R\), an increase in \(R\) leads to a decrease in \(P\). Therefore, both assertion and reason are true, and the reason correctly explains the assertion.

Power consumed by the external resistor (R) is \(P = I^2R = \left(\frac{E}{R+r}\right)^2 R\). Maximum power is delivered to the load when the external resistance equals the internal resistance R=r, according to the maximum power transfer theorem. Maximum current occurs when (R=0). Therefore, both Assertion (A) and Reason (R) are false.

The current in the circuit is \(I = E / (R + r)\). For \(I\) to be maximum, the denominator \((R + r)\) must be minimum. This occurs when \(r = 0\), not \(r = R\). So, Assertion (A) is false. The power produced across \(R\) is \(P_R = I^2 R = (E / (R + r))^2 R\). As \(r\) increases, \(R+r\) increases, so \(P_R\) decreases. Thus, \(P_R\) is minimum when \(r\) is maximum (approaching infinity), not at \(r = R\). So, Reason (R) is also false.

When a heavy current appliance is switched on, it draws a large current from the power supply. For a non-ideal source with internal resistance, this increased total current causes a larger voltage drop across the internal resistance of the source (or wiring). Consequently, the terminal voltage supplied to other devices like the light bulb decreases. A lower voltage across the bulb reduces its power output (\(P = V^2/R\)) and thus its brightness. So, Assertion (A) is true. Reason (R) correctly states that brightness remains constant for an ideal source and that voltage across the bulb decreases for a non-ideal source, which explains the dimming. Thus, Reason (R) is true and explains Assertion (A).

The power rating of a bulb is given by \(P = V^2 / R\). For bulbs rated at the same voltage \(V\) (here \(220 text{ V}\), resistance \(R = V^2 / P\). A lower power rating implies higher resistance. Thus, the \(20 \text{ W}\) bulb has the highest resistance (Reason R is true). When bulbs are connected in series, the same current \(I\) flows through each. The power dissipated by each bulb is \(P_{actual} = I^2 R\). Since \(I\) is common, the bulb with the highest resistance will dissipate the most power and therefore glow brightest. Hence, the \(20 \text{ W}\) bulb will provide maximum illumination (Assertion A is true). Reason (R) correctly explains Assertion (A).

Assertion (A) is true because heat produced is \( H = I^2 R t \) and the filament has a much higher resistance \( R \). Reason (R) is false because filaments (like tungsten) have a *high* melting point to withstand high temperatures.