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As we know from the nonlinear I-V characteristics of a filament lamp, that the resistance of a filament changes with change in current/voltage.

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From the relation V=IR, it should imply that, say with increase in current, the resistance should decrease, but at the same time V is increasing aswell. So, how to be certain that increase in V is more than that of I, such that R increases?

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The resistance of a particular component is defined to be the applied voltage divided by the resulting current. As you can see from the plot you attached, you can continue to increase V as much as you'd like, but the resulting current appears to saturate at some constant value. Therefore, the ratio $R = V/I$ increases with increasing $V$.

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  • $\begingroup$ So, this means, when I increase $I$, $V$ will increase by more amount, resulting in an increase in current, even with the increase of current. Ah, I get it. $\endgroup$
    – AgentRock
    Commented Aug 28, 2017 at 14:45

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