several electric bulbs designed to be used on a 220v electric supply line. are rate 10W. how many lamps can be connected in parallel with each other across the two wires of 220v line if the maximum allowable current is 5A???
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Several electric bulbs designed to be used on a 220 V electric supply line, are rated 10 W. How many lamps can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A?
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ANSWER
Given, V=220 V
Power rating of each bulb, P=10 W
Total current, I
t
=5 A
Let number of lamps in parallel be n.
Let individual resistance of each lamp be R.
From Joule's law of heating,
P=V
2
/R
10=220
2
/R
R=4840.............(i)
R
1
=R
2
=..............=R
n
=R..............(ii)
For resistances in parallel,
R
eq
1
=
R
1
1
+
R
2
1
+......+
R
n
1
........(iii)
From (ii) and (iii),
R
eq
=R/n..........(iv)
Substituting (i) in (iv),
R
eq
=4840/n...............(v)
From Ohm's Law,
V=I
t
R
eq
............(vi)
Substituting (v) in (vi),
220=5×4840/n
n=110