P28 082

background image

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.


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