A room is lighted by `200W,124 V` incandescent lamps fed by a generator whose output voltage is `130 V`. The conducting wires from the generator to the user are made of aluminimum wire of total length 150 m and cross-sectional area `15 mm^(2)`. How many such length can be installed ? What is the total power consumed by the user ? sp. resistance of aluminium is `2.9 xx 10^(-4) Omega m `

Answer

`12,2.4kW`

Explanation

Resistance of aluminium wire
`R_(Al) = (rho l)/(A) = (2.9 xx 10^(-8) xx 150)/( 15 xx 10^(-6)) = 0.29 Omega`
current through main line
`I = (130 - 124)/(0.29)= (20.69 )A`
Current through one lamp `l_(1) = (200)/(124) = 1.613 A` ltb rgt No of lamps `= (20.69)/(1.613) = 12.83 = 12.85`
Hence no of lamp to be used `= 12`
power connected `= 12 xx 200 = 2400 W= 2.4kW`