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Physics Chapter 11 : Topic 2
Potential Difference
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The expression $\left( \mathbf{V =}\frac{\mathbf{W}}{\mathbf{Q}} \right)$ defines:
Reasoning: Potential difference is defined as the work done per unit charge in moving a charge between two points.
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A potential difference of $\mathbf{1}$ volt exists between two points if:
Reasoning: By definition, $\mathbf{1V = 1\ J\ /\ C}$
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If $\mathbf{20\ J}$ of work is done in moving $\mathbf{4\ C}$ of charge, the potential difference is:
Reasoning: $\mathbf{V =}$ $\frac{\mathbf{W}}{\mathbf{Q}}\mathbf{=}\frac{\mathbf{20}}{\mathbf{4}}\mathbf{= 5}\mathbf{V}$
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The SI unit of potential difference is:
Reasoning: Potential difference is measured in volts $\mathbf{(V)}$.
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Which combination is equivalent to one volt?
Reasoning: $\mathbf{V =}$ $\frac{\mathbf{W}}{\mathbf{Q}}$ $\mathbf{\Longrightarrow}$ So, $\mathbf{1\ V = 1\ J\ /\ C}$
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For a fixed amount of work, the potential difference is:
Reasoning: $\mathbf{V =}$ $\frac{\mathbf{W}}{\mathbf{Q}}$ ; for constant $\mathbf{(W)}$, increasing $\mathbf{(Q)}$ decreases $\mathbf{(V)}$.
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A battery does $\mathbf{60\ J}$ of work in moving $\mathbf{12\ C}$ of charge. The potential difference across its terminals is:
Reasoning: $\mathbf{V =}$ $\frac{\mathbf{W}}{\mathbf{Q}}\mathbf{=}\frac{\mathbf{60}}{\mathbf{12}}\mathbf{= 5V}$
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If the potential difference between two points is doubled while the charge moved remains constant, the work done will:
Reasoning: $\mathbf{W = VQ}$ $\mathbf{\Longrightarrow}$ For constant $\mathbf{(Q)}$, doubling $\mathbf{(V)}$ doubles $\mathbf{(W)}$.
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Potential difference measures:
Reasoning: It represents energy transferred to each coulomb of charge.
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A charge of $\mathbf{3\ C}$ gains $\mathbf{18\ J}$ of energy when moved between two points. Thepotential difference is:
Reasoning: $\mathbf{V =}$ $\frac{\mathbf{18}}{\mathbf{3}}\mathbf{= 6\ V}$
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If no work is required to move a charge between two points, the potential difference between them is:
Reasoning: $\mathbf{V =}$ $\frac{\mathbf{W}}{\mathbf{Q}}$ $\mathbf{\Longrightarrow}$ If $\mathbf{W = 0}$, then $\mathbf{V = 0}$.
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A charge of $\mathbf{5\ C}$ moves through a potential difference of $\mathbf{10\ V}$. The work done is:
Reasoning: $\mathbf{W = VQ = (10)(5) = 50\ J}$
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Which physical quantity can be calculated directly using $\mathbf{V}\mathbf{=}$ $\frac{\mathbf{W}}{\mathbf{Q}}$?
Reasoning: The equation is the defining relation for potential difference.
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The potential difference between two points is $\mathbf{24\ V}$. How much work is required tomove $\mathbf{2\ C}$ of charge between them?
Reasoning: $\mathbf{W = VQ = (24)(2) = 48\ J}$
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If both work done and charge moved are doubled, the potential difference will:
Reasoning: $\mathbf{V =}$ $\frac{\mathbf{2W}}{\mathbf{2Q}}\mathbf{=}\frac{\mathbf{W}}{\mathbf{Q}}$
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A student claims that a higher voltage means more energy is supplied to each coulomb of charge. This statement is:
Reasoning: Voltage measures energy transferred per coulomb.
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The ratio $\mathbf{(W\ /\ Q)}$ remains constant for a given pair of points because:
Reasoning: The ratio gives the potential difference between those points.
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A charge of $\mathbf{0.5\ C}$ gains $\mathbf{4\ J}$ of energy. The corresponding potential difference is:
Reasoning: $\mathbf{V =}$ $\frac{\mathbf{W}}{\mathbf{Q}}\mathbf{=}\frac{\mathbf{4}}{\mathbf{0.5}}\mathbf{= 8\ V}$
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Which statement best describes a $\mathbf{12\ V}$ battery?
Reasoning: A $\mathbf{12\ V}$ battery transfers$\mathbf{12\ J}$ of energy to each coulomb of charge.
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If $\mathbf{100\ J}$ of work is required to move a charge between two points and the potential difference is $\mathbf{20\ V}$, the charge moved is:
Reasoning: $\mathbf{Q =}$ $\frac{\mathbf{W}}{\mathbf{V}}\mathbf{=}\frac{\mathbf{100}}{\mathbf{20}}\mathbf{= 5\ C}$
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The unit volt can also be expressed as:
Reasoning: Volt is the work done per unit charge.
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A charge gains more energy when moved through:
Reasoning: Since $\mathbf{(W = VQ)}$, greater $\mathbf{(V)}$ means more energy transfer for the same charge.
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Which graph would represent the relation $\mathbf{(W = VQ)}$ for constant $\mathbf{(V)}$?
Reasoning: Work is directly proportional to charge when voltage is constant.
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The equation $\left( \mathbf{V =}\frac{\mathbf{W}}{\mathbf{Q}} \right)$ shows that voltage is a:
Reasoning: Voltage is defined as energy transferred per unit charge and is a scalar quantity.
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A potential difference of $\mathbf{15\ V}$ means:
Reasoning: Voltage is energy transferred per unit charge.
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A source transfers $\mathbf{240\ J}$ of energy while moving $\mathbf{20\ C}$ of charge. The source voltage is:
Reasoning: $\mathbf{V =}$ $\frac{\mathbf{W}}{\mathbf{Q}}\mathbf{=}\frac{\mathbf{240}}{\mathbf{20}}\mathbf{= 12\ V}$
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Two charges, $\mathbf{2\ C}$ and $\mathbf{6\ C}$, are moved through the same potential difference. Comparing the work done:
Reasoning: $\mathbf{(W = VQ)}$For the same voltage, larger charge requires more work.
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Which quantity is a measure of electrical energy transferred?
Reasoning: Work done represents energy transferred in an electrical process.
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If a battery moves twice the charge while supplying the same energy, its potential difference becomes:
Reasoning: $\mathbf{V =}$ $\frac{\mathbf{W}}{\mathbf{Q}}$ $\mathbf{\Longrightarrow}$ Doubling $\mathbf{Q}$ with constant $\mathbf{W\ }$halves $\mathbf{V}$.
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The most complete interpretation of electric potential difference is:
Reasoning: Potential difference is defined as the work done or energy transferred per coulomb of charge.
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