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Physics Chapter 11 : Topic 14
Potentiometer Principle
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The basic principle of a potentiometer is based on the fact that the potential drop across a uniform wire is:
Reasoning: For a uniform wire carrying constant current, potential drop increases uniformly with length.
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The potential gradient of a potentiometer wire is defined as:
Reasoning: Potential gradient is the rate of change of potential with distance along the wire. $\mathbf{\Longrightarrow}$ $\mathbf{k =}$ $\frac{\mathbf{V}}{\mathbf{L}}$
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The main purpose of a potentiometer is to:
Reasoning: A potentiometer compares $\mathbf{EMFs}$ or potential differences without drawing current from the source being measured.
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The principle of a potentiometer states that the potential difference across a length of wire is proportional to:
Reasoning: For a uniform wire with constant current $\mathbf{\Longrightarrow}$ $\mathbf{V \propto I}$
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In a potentiometer experiment, the balancing point is the point where:
Reasoning: At balance point, no current flows through the galvanometer because potential difference between two points becomes zero.
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The sensitivity of a potentiometer can be increased by:
Reasoning: A smaller potential gradient gives a larger balancing length, making measurements more sensitive.
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Two cells are compared using a potentiometer. If their balancing lengths are $\mathbf{L}_{\mathbf{1}}\mathbf{\ }$and $\mathbf{L}_{\mathbf{2}}$, their $\mathbf{EMFs}$ are related as:
Reasoning: Since $\mathbf{EMF}$ is proportional to balancing length. $\mathbf{\Longrightarrow}$ $\frac{\mathbf{E}_{\mathbf{1}}}{\mathbf{E}_{\mathbf{2}}}\mathbf{=}\frac{\mathbf{L}_{\mathbf{1}}}{\mathbf{L}_{\mathbf{2}}}$
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A potentiometer is preferred over a voltmeter for comparing $\mathbf{EMFs}$ because it:
Reasoning: At balance point, the potentiometer does not draw current from the cell, giving accurate measurements.
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If the balancing length of a cell increases, its $\mathbf{EMF}$:
Reasoning: $\mathbf{EMF}$ is directly proportional to balancing length ; $\mathbf{E = k}\mathbf{l}$ $\mathbf{\Longrightarrow}$ $\mathbf{E}\mathbf{\propto}\mathbf{l}$
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A potentiometer wire should be uniform because:
Reasoning: Uniform resistance per unit length ensures a constant potential gradient.
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If a wire of a potentiometer has length $\mathbf{10\ m}$ and potential difference $\mathbf{5\ V}$ across it, the potential gradient is:
Reasoning: $\mathbf{k =}$ $\frac{\mathbf{V}}{\mathbf{L}}\mathbf{=}\frac{\mathbf{5}}{\mathbf{10}}\mathbf{= 0.5\ V/m}$
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In a potentiometer circuit, the driving cell is used to:
Reasoning: The driving cell establishes a uniform potential drop along the potentiometer wire.
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The balance condition in a potentiometer means:
Reasoning: At balance, the potential drop along the wire equals the $\mathbf{EMF}$ being measured.
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A potentiometer measures $\mathbf{EMF}$ more accurately than a voltmeter because a voltmeter:
Reasoning: A voltmeter draws a small current, causing terminal voltage to differ from $\mathbf{EMF}$.
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If the current through a potentiometer wire is increased, the potential gradient:
Reasoning: Increasing current increases voltage drop across the wire, increasing potential gradient.
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A jockey is used in a potentiometer to:
Reasoning: The jockey makes contact at different positions to find the balance point.
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At the balance point of a potentiometer, the galvanometer shows:
Reasoning: No current flows through the galvanometer at balance.
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Two cells have balancing lengths of $\mathbf{40\ cm}$ and $\mathbf{60\ cm}$. The ratio of their $\mathbf{EMFs}$ is:
Reasoning: $\frac{\mathbf{E}_{\mathbf{1}}}{\mathbf{E}_{\mathbf{2}}}\mathbf{=}\frac{\mathbf{L}_{\mathbf{1}}}{\mathbf{L}_{\mathbf{2}}}\mathbf{=}\frac{\mathbf{40}}{\mathbf{60}}\mathbf{=}\frac{\mathbf{40}}{\mathbf{60}}\mathbf{=}\frac{\mathbf{2}}{\mathbf{3}}$
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The $\mathbf{EMF}$ of a cell using a potentiometer is determined by measuring:
Reasoning: The $\mathbf{EMF}$ is proportional to the length at which balance occurs.
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If the length of potentiometer wire is doubled while maintaining the same voltage, the potential gradient:
Reasoning: $\mathbf{k =}$ $\frac{\mathbf{V}}{\mathbf{L}}$ $\mathbf{\Longrightarrow}$ Increasing length reduces potential gradient.
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In comparing two $\mathbf{EMFs}$ using a potentiometer, the current through the potentiometer wire should be:
Reasoning: Constant current ensures constant potential gradient.
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A potentiometer works on the principle of:
Reasoning: The potential drop is uniformly distributed along the potentiometer wire.
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A cell with greater $\mathbf{EMF}$ will have:
Reasoning: Greater $\mathbf{EMF}$ requires a larger potential drop, which occurs over a longer wire length.
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If the potentiometer wire becomes non-uniform, then:
Reasoning: Non-uniform resistance causes an uneven potential gradient.
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The ratio of $\mathbf{EMFs}$ measured by potentiometer is independent of:
Reasoning: The ratio depends only on balancing lengths. $\mathbf{\Longrightarrow}$ $\frac{\mathbf{E}_{\mathbf{1}}}{\mathbf{E}_{\mathbf{2}}}\mathbf{=}\frac{\mathbf{L}_{\mathbf{1}}}{\mathbf{L}_{\mathbf{2}}}$
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A potentiometer can measure the internal resistance of a cell because it can compare:
Reasoning: Difference between $\mathbf{EMF}$ and terminal voltage helps determine internal resistance.
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A longer potentiometer wire improves accuracy because:
Reasoning: Lower potential gradient allows more precise measurement of small voltage differences.
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The null method used in a potentiometer means:
Reasoning: The measurement is made when the galvanometer shows no deflection.
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If the potential gradient of a potentiometer is $\mathbf{0.02\ V/cm}$ and balance length is $\mathbf{50\ cm}$, the $\mathbf{EMF}$ is:
Reasoning: $\mathbf{E =}\mathbf{kl}\mathbf{= 0.02 \times 50 = 1\ V}$
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The main advantage of a potentiometer over a voltmeter is that it:
Reasoning: The null method provides accurate measurements because the source under test supplies no current at balance.
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