Question

two bulbs A and B are rated 100 W 120V and 10W 120V respectively. they are connected in parallel series across a 120 V source. find the current each bulb.​

Answer 1

Correct Question :

Two bulbs A and B are rated 100 W 120V and 10W 120V respectively. They are connected in series across a 120 V source. Find the current of each bulb.

Solution :

(Remeber that, in parallel current is same and in series voltage is same.)

For bulb A :-

Power = 100 W

Voltage = 120 V

So,

=> $R_{A}$ = $\dfrac{ {V}^{2} }{P}$

=> $R_{A}$ = $\dfrac{ {(120)}^{2} }{100}$

=> $R_{A}$ = $\dfrac{14400}{100}$

=> $R_{A}$ = 144 _________ (eq 1)

For bulb B :-

Power = 10 W

Voltage = 120 V

So,

=> $R_{B}$ = $\dfrac{ {V}^{2} }{P}$

=> $R_{B}$ = $\dfrac{ {(120)}^{2} }{10}$

=> $R_{B}$ = $\dfrac{14400}{10}$

=> $R_{B}$ = 1440 _________ (eq 2)

Now, both bulbs are connected in series.

So,

$R_{S}$ = $R_{A}$ + $R_{B}$

=> $R_{S}$ = 144 + 1440

=> $R_{S}$ = 1584 ohm.

Now,

$P \: = \: {I}^{2}R$

For bulb A :-

=> $100 \: = \: {I}^{2}(1584)$

=> ${I}^{2}\:=\:\dfrac{100}{1584}$

=> ${I}^{2}\:=\:0.0631$

=> $I\:=\:0.25\:A$

For bulb B :-

=> $10 \: = \: {I}^{2}(1584)$

=> ${I}^{2}\:=\:\dfrac{10}{1584}$

=> ${I}^{2}\:=\:0.00631$

=> $I\:=\:0.079\:A$