Three parallel-plate capacitors are connected in series to an adjustable high-voltage…

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Force Field and Potential · Electric Force Field and Potential

Problem

Three parallel-plate capacitors are connected in series to an adjustable high-voltage dc source. Their capacitances and plate separations are listed below. •

C_{1}=1.0\,\mu\text{F}

, plate separation

d_{1}=0.20\,\text{mm}

•

C_{2}=0.60\,\mu\text{F}

, plate separation

d_{2}=0.12\,\text{mm}

•

C_{3}=0.30\,\mu\text{F}

, plate separation

d_{3}=0.08\,\text{mm}

The dielectric material in each capacitor breaks down if the electric field magnitude within it reaches

3.0\times10^{7}\,\text{V}\,\text{m}^{-1}

. (a) Express the electric field magnitude in each capacitor in terms of its potential difference and plate separation. (b) Derive, in symbolic form, an expression for the potential difference across each capacitor as a function of the applied battery voltage

V_{\text{bat}}

. (c) Using your result from part (b), determine the maximum value of

V_{\text{bat}}

that can be applied without causing dielectric breakdown in any capacitor. (d) Identify which capacitor reaches the breakdown threshold first as the battery voltage is increased and explain why.

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