Between A and B, direct 20 Ω is in parallel with path A–C–B (50 + 30 = 80 Ω), so Req = (20×80)/(20+80) = 16 Ω.

Shunt resistances for current measurement are connected in parallel with the galvanometer to extend range.

Switching from series to parallel with three equal resistors increases power by a factor of 9, so 20 W × 9 = 180 W.

Using the given circuit values (current and resistances) and V = IR across the section between A and B yields 1.5 V (option A).

A voltmeter requires a large series resistance with the galvanometer so only a small current flows and the voltage across the instrument can be measured.

R1∝20, R2∝30 so R_parallel = (20×30)/(20+30) =12 (in same units), hence time ∝12 minutes.

According to the circuit labeling and the given switch positions, closing S1 connects the nodes to the 15 V and 20 V supplies respectively, making V1 = 15 V and V2 = 20 V.

Impedance Z = V/I = 100 V / 0.1 A = 1000 Ω.

Manganin is used for resistance boxes because it has a low temperature coefficient and stable resistivity.

At parallel resonance the circuit impedance is high and the voltage across the circuit (or branch) reaches a maximum.