Question

If we connect n bulbs each with a rated power P in parallel, what is the total power consumed by combination at rated voltage ?​

Answer 1

Let resistance each bulb =R and voltage of source =V

Power of each bulb is P=V  2  /R or R=V  2  /P

As n bulbs are in series so total resistance R  t

​   =nR and current i=V/R  t

​   =V/nR

Total power drawn is P  t

​   =i  2  R  t ​   =  n  2  R  2   V  2   ​   (nR)=  nR V  2 =P/n

Answer 2

Electricity

There are n bulbs each with a rated power P in parallel.

Let the resistance of each Bulb be R.

When resistors are in parallel, then, we got ,

$\frac{1}{R_p}= \frac{1}{R_1}+ \frac{1}{R_2}+\_+\_+ \frac{1}{R_n}$

As we know that,

$P=V^2/R$

$\implies \frac{P_p}{V^2}= \frac{P_1}{V^2}+ \frac{P_2}{V^2}+\_+\_+ \frac{P_n}{V^2}$

$\implies P_p=P_1+P_2+\_+\_+P_n$

$\implies P_p=nP$

Hence, nP will be the total power consumed by combination at the rated voltage when n bulbs will be connected with a rated power P in parallel.