Answer:
Let, R be the resistance of the heater wire. Since, two heater wires are of equal length their resistance is also same.
Hence, for series combination of resistances,
R
s
=2R
And for parallel combination of resistances,
R
p
=
2
R
Now, heat produced when they first connected in series is
H
s
=
R
s
V
2
where, V is voltage supplied to the heater.
H
s
=
2R
V
2
.....................................(1)
heat produced when they first connected in series is
H
p
=
R
p
V
2
H
p
=
2
R
V
2
H
p
=
R
2V
2
............................................(2)
From (1) and (2), we get
H
p
H
s
=
R
2V
2
2R
V
2
⇒
H
p
H
s
=
4
1
