Question

n identical bulbs are rated P watt and V volt when they are connected in series total power consumed is 20 watt and when they are connected in parallel they consume total power of 2000 watt how many bulbs are used​

Answer 1

Given:

n identical bulbs are rated P watt and V volt when they are connected in series total power consumed is 20 watt and when they are connected in parallel they consume total power of 2000 watt.

To find:

Number of bulbs used .

Calculation:

When resistances are connected in parallel , the total power is equivalent to the algebraic addition of individual powers of the resistance.

$\therefore \: 2000 = P + P + .....n \: times$

$= > \: nP = 2000$

When resistances are connected in series , the reciprocal of the total power is equivalent to the addition of reciprocal of individual powers.

$\therefore \: \dfrac{1}{20} = \dfrac{1}{P} + \dfrac{1}{P} + .... \: n \: times$

$= > \: \dfrac{1}{20} = \dfrac{n}{P}$

$= > \dfrac{P}{n} = 20$

Dividing the two equations :

$\therefore \: \dfrac{nP}{ (\frac{P}{n}) } = \dfrac{2000}{20}$

$= > {n}^{2} = 100$

$= > n = 10 \: bulbs$

So , final answer is:

10 Bulbs were used in the circuit.