Two tungsten lamps with resistances `R_(1) and R_(2)`, respectively , are connected first in parallel and then in series in a lighting circuit of negligible internal resistance. Given `R_(1) gt R_(2)`.
(a) Which lamp will glow more brightly when they are connected in parallel ?
(b) If the lamps of resistance `R_(1)` now burns out, how will the net illumination produced change ?
(c ) Which lamp will glow more brightly when they are connected in series ?
(d) If the lamp of resistance `R_(2)` now burns out and lamp `R_(1)` alone is plugged in , will the net illumination increase or decrease ?

Explanation

(a) When the bulbs are in series, current I = constant. As `P = I^(2) R, so P prop R`. Hence the lamp with higher resistance (i.e., `R_(1)`) will glow more brightly.
(b) When the two bulbs are operating in series, total illumination, `P = V^(2)/(R_(1)+R_(2))`
When the lamp of resistance `R_(2)` gets burned and bulb of resistance `R_(1)` alone is operated,then illumination, `P' =V^(2)/R_(1)`, i.e., `P' gt P`
So the net illumination will increase.
(c ) When the bulbs are in parallel, voltage across each bulb is same. As, `P = V^(2)/R, so P prop 1/R`
Hence, the lamp with lesser resistance, i.e., `R_(2)` will glow more brightly.
(d) When both the bulbs are operating in parallel, then the total illumination,
`P = P_(1) + P_(2) = V^(2)/R_(1) + V^(2)/R_(2)`
When lamp of resistance `R_(1)` burns out, only lamp of resistance `R_(2)` will give light. Then illumination is , `P' = V^(2)/R_(2), i.e., P' lt P`
So the net illumination will decrease.