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Question

The current-voltage graph for a device is shown in figure. The resistance is negative in region.
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A
AB
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B
BC
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C
ABC
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D
None of these
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Solution

The correct option is A AB
According to the Ohm's law, the resistance is the voltage applied across resistor per unit current passing through it.
R=VI
Hence R=1I/V
R=1slope
Hence resistance is negative when the slope of the curve is negative.
Therefore resistance is negative in region AB.

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Q. Note that for nearly all materials the current - voltage relation is temperature dependent. Thus at low temperatures the curve in Fig. (a) rises more steeply for positive V than at higher temperatures, and at successively higher temperatures the asymmetry in the curve becomes less and less pronounced.
The current - voltage relation for a source may also be represented graphically. For a source represented by Vab=EIr, that is, V=EIr, The graph appears in Figure (b). The intercept on the Vaxis, corresponding to the open circuit condition (I=0), is at V=E, and the intercept on the Iaxis, corresponding to a short-circuit situation (V=0), is at I=Er.
This relation may be used to find the current in a circuit containing a non linear device, as in fig (c). Its current voltage relation is shown in fig (d) and terminal voltage V=EIr is also plotted on this graph, each curve represents a current-voltage relation that must be satisfied, so the intersection represents the only possible values of V and I. This amounts to a graphical solution of two simultaneous equation of V and I, one of which is nonlinear.
When a device has a nonlinear voltage-current relation, the quantity VI is not constant. This ratio may still be called resistance, but now it varies with current; it is constant only for a device obeying Ohm's law. Often a more useful quantity is dVdI, which expresses the relation between a small change in current and the resulting voltage change. This is called dynamic or incremental resistance. Which of the following vacuum tube devices shows negative resistance?
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