Question

A circuit has a line of 5A. how many lamps of rating 40W;220V can simultaneously run on this line safely

Answer 1

power rating of bulb is 40watts and 220v
resistance of bulb,
R=V²/p
⇒220*220/40
⇒1210ohms
maximum voltage=220v
maximum current= 5 amp.
Maximum resistance, when 'n' no of resistances are connected in parallel.
R₁=v/I
⇒220/5
⇒44 ohms
Net resistance=R₁=r/n
⇒44=1210/n
n=27.5
so 27 bulbs we can light.

Answer 2

H=I²Rt (H is directly proportional to R)

P=V²/R(P is inversely proportional to 1/R)

40=220×220/R
R=220×220/40
R=110×11

$\green{R=1210Ω}$

Max. no. of Resistance(n) to be connected

r=V/I
r=220/5

${\green{r=44}}$

Net Resistance

r=R/n
n=R/r
n=1210/44

${\green {n=27.5}}$

${\textbf{\blue{Hence we can connect 27 lamps safely.}}}$

Hope it helps :)