Question

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 series with each other across the two wires of 220 V line if the maximum current allowed is 5 A?​

Answer 1

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