SAT II Physics : Capacitors

Study concepts, example questions & explanations for SAT II Physics

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Example Questions

Example Question #2 : Electricity And Magnetism

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:

\(\displaystyle C^{2}\)

\(\displaystyle \frac{1}{C}\)

\(\displaystyle \frac{1}{2}C\)

\(\displaystyle 2C\)

\(\displaystyle C\)

Correct answer:

\(\displaystyle \frac{1}{2}C\)

Explanation:

Capacitance of a circuit is defined by the equation:

\(\displaystyle C=\varepsilon\frac{A}{d}\)

Where \(\displaystyle C\) is the capacitance, \(\displaystyle \varepsilon\) 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 \(\displaystyle \frac{1}{2}A\) in for \(\displaystyle A\)

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

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