82. The part of R
0
connected in parallel with R is given by R
1
= R
0
x/L, where L = 10 cm. The voltage
difference across R is then V
R
=
ER
/R
eq
, where R
= RR
1
/(R + R
1
)and R
eq
= R
0
(1
− x/L) + R
.
Thus
P
R
=
V
2
R
R
=
1
R
ERR
1
/(R + R
1
)
R
0
(1
− x/L) + RR
1
/(R + R
1
)
2
.
Algebraic manipulation then leads to
P
R
=
100R(
Ex/R
0
)
2
(100R/R
0
+ 10x
− x
2
)
2
where x is measured in cm.