26. Capacitors & Dielectrics

Parallel Plate Capacitors

Parallel Plate Capacitor Physics Problems

Anderson Video - Electric Field Energy Density

 We need to know the area of the plates to answer this question. 

 A parallel plate capacitor is charged up using a battery. The battery is then removed, and the plate separation is increased by somebody wearing insulating gloves. What happens to the potential difference between the plates? 

<p>Two circular plates of radius 2cm are brought together so their separation is 5mm. What is the capacitance of these plates?</p>

 A parallel plate capacitor consists of two circular plates of radius 12 cm separated by <math display=“inline”><mrow><mn>0</mn><mo>.</mo><mrow><mn>23</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">mm</mi></mrow></mrow></math>. What is the electric field strength inside the capacitor when the plates carry a charge of <math display=“inline”><mrow><mn>14</mn><mtext>&#x00A0;</mtext><mi>&#x00B5;</mi><mi mathvariant="normal">C</mi></mrow></math>? 

<p>A 3 F capacitor is given a potential difference across its plates of 10 V. What is the charge built up on its plates? If the source of the potential difference across the plates is removed, but the plates maintain their charge, what is the new potential difference across the capacitor if the distance between the plates is doubled?</p>

 One gallon of typical gasoline has 132 MJ of energy. You wish to store that much energy in a parallel-plate capacitor for an electric car. Assume you charge the capacitor using a <math display=“inline”><mrow><mn>120</mn><mtext>&#x00A0;</mtext><mi mathvariant="normal">V</mi></mrow></math> power source. You can fill the capacitor with any of the materials listed in Table 21.3, but the spacing between plates has to be 0.080 mm. What is the minimum surface area required for the capacitor? This may help to understand challenges in engineering electric cars. 

Point Charge Inside Capacitor

The Parallel Plate Capacitor Equation

 What is the capacitance of a parallel plate capacitor with plate area <math display='inline'><mrow><mn>2500</mn><mo rspace="thickmathspace">&#x2062;</mo><msup><mi mathvariant="normal" class="MathML-Unit">cm</mi><mn>2</mn></msup></mrow></math> separated by a distance <math display='inline'><mrow><mn>0.10</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">mm</mi></mrow></math>? 

 What is the smallest possible capacitance of a parallel-plate capacitor with plate area <math display=“inline”><mrow><mn>2500</mn><msup><mrow><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow><mn>2</mn></msup></mrow></math> separated by a distance <math display=“inline”><mrow><mn>0</mn><mo>.</mo><mrow><mn>10</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">mm</mi></mrow></mrow></math>, if you can fill it with any of the materials listed in Table 21.3? 

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