Question:
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:
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:
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Current is proportional to drift velocity, and E = V/l; find how V depends on I.
Updated On: Nov 11, 2026
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The Correct Option is C
Solution and Explanation
\(I = n e A v_d \propto \sqrt{E}\) and \(E = V/l\), so \(I \propto \sqrt{V}\).
Hence \(V \propto I^2\): a parabola through the origin, concave upward (V increases faster than linearly with I).
Option (1) is a peak curve, (2) is concave downward (\(V\propto\sqrt I\)), (4) is linear (ohmic), (3) is the upward-curving parabola.
Answer: (3) the upward-curving (parabolic) V-I graph
Hence \(V \propto I^2\): a parabola through the origin, concave upward (V increases faster than linearly with I).
Option (1) is a peak curve, (2) is concave downward (\(V\propto\sqrt I\)), (4) is linear (ohmic), (3) is the upward-curving parabola.
Answer: (3) the upward-curving (parabolic) V-I graph
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