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Q. 74

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

A vacuum-insulated parallel-plate capacitor with plate separation has capacitance . What is the capacitance if an insulator with dielectric constant and thickness is slipped between the electrodes without changing the plate separation?

If an insulator with dielectric constant and thickness is slipped between the electrodes without changing the plate separation then the capacitance is

See the step by step solution

Step by Step Solution

Step 1: Given Information

Parallel-plate capacitor with plate separation

Capacitance

Dielectric constant

Thickness

Step 2: Explanation

If we insert an insulator into such a capacitor with separation and , then we can treat it as two capacitors connected in series, each with thickness and

It is clear that the capacitance of the air half will be

Since the capacitance is given as

The capacitance of the other half will then clearly be

Resulting capacitance of the considered system will be

The resulting capacitance will be

Step 3: Final Answer

Hence, the capacitance is

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