Q. 74

Expert-verifiedFound in: Page 741

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

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

Parallel-plate capacitor with plate separation

Capacitance

Dielectric constant

Thickness

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

Hence, the capacitance is

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