Bukhovtsev-et-al-Problems-in-Elementary-Physics

ELECTRICITY AND MAGNETISM 321
Fig. 436 Fig. 437
According to Ohm's law,
and finally
/lR x = / 2l 1 ~ and /lR o=/'},12 ~
where p is the resistivity and A is the cross section of the slide wire.
R 1
Therefore, R: = 1:
470. Such a resistance r should be connected between points C and D that
the resistance of the last cell (Fig. 436) is also r, In this case the last cell
can be rep laced by the resistance r, then the same can be done with the next
to last cell, etc. Now the total resistance of the circuit will not depend on
the number of cells and will be equal to r,
The following equation can be written for r:
(2R+r) R r
3R+r
Hence, r=R(Y3-1)~O.73R.
471. The last cell is a voltage divider that reduces the potential of the ~-th
point k times as compared with the (n-l)th point. Hence, Un=
U n -
= R +R 1 R U n - 1 1 k 1 ( P' 437)
3 =-k-' or
1 s
R = - see 19. ·
3
The relation Uj= U~-1 should be true for any cell. For this reason the
'resistance of the last cell, of the last two. of the last three, etc .• cells should
,also be R 3 (see Problem 470). Therefore,
..!.-=..!-+ 1
e, R 2 R 1 +R 3
R Rs (R1 +Rs) R
2 a
.s:
R 1 k-l
R 1 : R 2 : R s = (k- l )2:k :(k- l )
472. Devices whose action is based, for example, on the deflection of a
current-carrying conductor in a magnetic field cannot be used. The angle
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