Question

several electric bulbs designed to be used on a 228v electric supply lines are rated at 10w. how many lamps can be connected in parallel with each other across the two wires of 220v lines if the maximum allowed current in 5a

Answer 1

$hey \:mate \: here \: is \: ur \: answer$
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$given \: V = 220V$

$power \: rating \: of \: each \: bulb \: P = 10W$



$total \: current \: It= 5 A$



$let \: number \: of \: lamps \: in \: parallel \: be \: n$


$let \: individual \: resistance \: of \: each \: lamp \: be \: R$



$from \: joules \: law \: of \: heating \:$



$P = \frac{ {V}^{2} }{R}$
$10 = \frac{ {220}^{2} }{R}$

$R= 4840................1$


$R1 = R2 = ........... = Rn = R.....2$


$for \: resisatance \: in \: parallel \\ \\ \frac{1}{Req} = \frac{1}{R1} = \frac{1}{R2} + ....... \frac{1}{Rn}..........3$


$from \: 2and \: 3$
$Req = \frac{R}{n} ..........4$


$substituting \: 1 \: in \: 4$


$Req = \frac{4840}{n} ...........5$


$from \: ohm's \: law \: \\ \\ \\ v = ItReq...........6$



$substituting \: 5 \: in \: 6$
$220 = \frac{5 \times 4840}{n}$

$n = 110$

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Hope this helps you!!! ^_^
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