Three bulbs B2, B, and B, having rated powers 100 W, 60 W
and 60 W at 250 V are connected in a circuit as shown in the
adjacent figure. if W1, W2, and W3 are the output powers of the
bulbs B2, B, and B2 respectively, then
(A) W1 > W2 = W3
(B) W1 > W2 > W3
(C) W1 < W2 = W3
(D) W1 < W2 < W3
Answers
Answer:Resistance is given by R=
P
V
2
∴ Resistance of 100 W bulb is given by
R
1
=
100
V
2
=
100
(250)
2
.....(i)
Similarly, resistance of 60 W bulbs each is given by
R
2
=R
3
=
60
V
2
=
60
(250)
2
.....(ii)
Output power of bulb B
1
is given by
W
1
=I
2
R
1
=(
R
1
+R
2
V
)
2
R
2
=
(R
1
+R
2
)
2
V
2
R
1
....(iii)
Similarly, output power of bulbs B
2
,B
3
respectively are given by
W
2
=
(R
1
+R
2
)
2
V
2
R
2
....(iv)
W
3
=
R
3
V
2
....(v)
From (iii) and (iv), we get
W
2
W
1
=
R
2
R
1
....(v)
Substituting the values of R
1
,R
2
from equations (i) and (ii) and on solving we get
W
3
W
2
=
25
15
.....(vi)
From (iv) and (v), we get
W
3
W
2
=
(R
1
+R
2
)
2
R
2
R
3
Substituting the values of R
1
,R
2
,R
3
from eqn. (i) and (ii) on solving, we get.
W
3
W
2
=
64
25
....(viii)
from eqn. (vi) and (vii), we have
W
1
:W
2
:W
3
=15:25:64⇒W
1
<W
2
<W
3
.
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