Question 19

Suppose the drift velocity $$v_d$$ in a material varied with the applied electric field E as $$v_d \propto \sqrt{E}$$. Then V - I graph for a wire made of such a material is best given by:

$$I = nAev_d$$

$$E = \frac{V}{l}$$. For a fixed length, $$E \propto V$$

$$v_d \propto \sqrt{E}$$

Substituting the proportionalities $$I \propto v_d$$ and $$E \propto V$$ into the above condition:

$$I \propto \sqrt{V}$$

$$I^2 \propto V \implies \mathbf{V = kI^2}$$

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