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Physics Chapter 11 : Topic 1
Current and Drift Velocity
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The expression $\mathbf{(I = Anvq)}$ shows that electric current in a conductor depends directly on:
Reasoning: According to $\mathbf{(I = Anvq)}$, current depends on cross-sectional area $\mathbf{(A)}$, number density $\mathbf{(n)}$, drift velocity $\mathbf{(v)}$ and charge $\mathbf{(q)}$.
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If the drift velocity of charge carriers in a wire is doubled while all other quantities remain unchanged, the current becomes:
Reasoning: Since $\mathbf{I \propto v}$, doubling drift velocity doubles the current.
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A wire carries current due to electrons moving with drift velocity $\mathbf{(v)}$. If the number density of electrons is doubled, the current will:
Reasoning: Current is directly proportional to $\mathbf{(n)}$, so doubling $\mathbf{(n)}$ doubles $\mathbf{(I)}$.
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Two wires of the same material carry charge carriers with the same drift velocity. The second wire has twice the cross-sectional area of the first. The current in the second wire is:
Reasoning: $\mathbf{I \propto A}$, so doubling area doubles current.
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The quantity $\mathbf{(n)}$ in $\mathbf{(I = Anvq)}$ represents:
Reasoning: $\mathbf{(n)}$ is the number density of free charge carriers.
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The SI unit of $\mathbf{(n)}$ is:
Reasoning: Number density means number per unit volume, so unit is $\mathbf{m}^{\mathbf{- 3}}$.
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Which quantity has the SI unit coulomb $\mathbf{(C)}$ in the equation $\mathbf{(I = Anvq)}$?
Reasoning: $\mathbf{(q)}$ is the charge carried by each carrier and is measured in coulombs.
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A wire carries current because electrons drift through it. The current will increase if:
Reasoning: Increasing area increases the number of charge carriers crossing per second.
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For a metallic conductor, the charge carrier is usually:
Reasoning: Free electrons are responsible for conduction in metals.
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The product $\mathbf{(nv)}$ physically represents:
Reasoning: $\mathbf{(nv)}$ gives the number of carriers moving through unit area each second.
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A conductor has area $\mathbf{(A)}$ and carries current $\mathbf{(I)}$. If both $\mathbf{(A)}$ and $\mathbf{(v)}$ are doubled, current becomes:
Reasoning: $\mathbf{I \propto Av}$ $\mathbf{\Longrightarrow}$ Doubling both gives $\mathbf{2 \times 2 = 4}$ times current.
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A current of $\mathbf{2\ A}$ flows through a wire. If the charge on each carrier remains unchanged and the drift velocity becomes half, the same current can be maintained by:
Reasoning: Since $\mathbf{I \propto nv}$, halving $\mathbf{(v)}$ requires doubling $\mathbf{(n)}$.
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The expression $\mathbf{(I = Anvq)}$ is derived from the idea that current is:
Reasoning: Current is defined as the rate of flow of charge.
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If electrons move with drift velocity $\mathbf{(v)}$, increasing temperature generally causes current to decrease for a fixed voltage because:
Reasoning: Higher temperature increases collisions, reducing drift velocity.
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Which factor does NOT appear explicitly in $\mathbf{(I = Anvq)}$?
Reasoning: Resistance is not directly present in this microscopic current equation.
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If a wire is stretched so that its area decreases to half while $\mathbf{(n)}$, $\mathbf{(v)}$ and $\mathbf{(q)}$ remain constant, the current becomes:
Reasoning: Current is directly proportional to area.
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A current-carrying wire contains charge carriers of charge $\mathbf{(2e)}$ instead of $\mathbf{(e)}$. For the same $\mathbf{(A)}$, $\mathbf{(n)}$ and $\mathbf{(v)}$, the current will be:
Reasoning: $\mathbf{I \propto q}$, so doubling charge doubles current.
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Which change would increase current the MOST?
Reasoning: Current becomes $\mathbf{2 \times 2 = 4}$ times greater.
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Two conductors carry the same current. The first has twice the number density of charge carriers as the second. If all other quantities are equal, the drift velocity in the first conductor is:
Reasoning: For constant current, $\mathbf{(nv)}$ must remain constant. Doubling $\mathbf{(n)}$ halves $\mathbf{(v)}$.
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A wire has current $\mathbf{(I)}$. If $\mathbf{(A)}$ becomes three times and $\mathbf{(n)}$ becomes one-third while $\mathbf{(v)}$ and $\mathbf{(q)}$ remain constant, the new current is:
Reasoning: $\mathbf{I \propto An}$ $\mathbf{\Longrightarrow}$ Multiplying by $\mathbf{3}$ and then by $\mathbf{1\ /\ 3}$ gives no change.
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The microscopic form $\mathbf{(I = Anvq)}$ helps explain current in terms of:
Reasoning: The equation relates current to the movement of charge carriers inside the conductor.
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A conductor carries current because:
Reasoning: Current arises from the directed motion (drift) of charge carriers.
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For a given current, if the cross-sectional area is reduced, the drift velocity must:
Reasoning: Since $\mathbf{(I = Anvq)}$, reducing $\mathbf{(A)}$ requires an increase in $\mathbf{(v)}$ to keep $\mathbf{(I)}$ constant.
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The equation $\mathbf{(I = Anvq)}$ is most useful for relating macroscopic current to:
Reasoning: It connects measurable current with carrier density, charge, and drift velocity inside the conductor.
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The drift velocity in a metal is typically:
Reasoning: Drift velocity is usually of the order of $\mathbf{mm/s}$ or less.
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