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SAT II Physics : Capacitors

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Example Question #1 : Electricity

A capacitor with capacitance $\displaystyle C$ is constructed by putting a thin piece of cardboard between two copper plates, then each plate is connected to a battery. If the copper plates are cut in half then what is the effect on the capacitance of the circuit?

Possible Answers:

$\frac{1}{2}C$ $\displaystyle \frac{1}{2}C$

$\displaystyle C$

$C^{2}$ $\displaystyle C^{2}$

$\frac{1}{C}$ $\displaystyle \frac{1}{C}$

$\displaystyle 2C$

Correct answer:

$\frac{1}{2}C$ $\displaystyle \frac{1}{2}C$

Explanation:

Capacitance of a circuit is defined by the equation:

$C=\varepsilon\frac{A}{d}$ $\displaystyle C=\varepsilon\frac{A}{d}$

Where $\displaystyle C$ is the capacitance, $\varepsilon$ $\displaystyle \varepsilon$ is a constant of nature, $\displaystyle A$ is the area of the capacitor, and $\displaystyle d$ is the distance between the two plates

Since the metal plates are cut in half, the area is halved. We can substitute $\frac{1}{2}A$ $\displaystyle \frac{1}{2}A$ in for $\displaystyle A$

The result is that the capacitance is half the original quantity.

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SAT II Physics : Capacitors

Study concepts, example questions & explanations for SAT II Physics

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Example Question #1 : Electricity

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