2.24 What is the area of the plates of a 2 F parallel plate capacitor, given that the separation between the plates is 0.5 cm? [You will realize from your answer why ordinary capacitors are in the range of μF or less. However, electrolytic capacitors do have a much larger capacitance (0.1 F) because of very minute separation between the conductors.]

<p><strong>2.24 </strong>Capacitance of the parallel capacitor, C = 2 F</p><p>Distance between two plates, d = 0.5 cm = 0.5&nbsp;<span title="Click to copy mathml"><math><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>2</mn></mrow></mrow></msup></math></span>&nbsp;m</p><p>Capacitance of a parallel plate capacitor is given by the relation,</p><p>C =&nbsp;<span title="Click to copy mathml"><math><mfrac><mrow><mrow><msub><mrow><mrow><mi>ε</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub><mi>A</mi></mrow></mrow><mrow><mrow><mi>d</mi></mrow></mrow></mfrac></math></span>&nbsp;, where&nbsp;<span title="Click to copy mathml"><math><msub><mrow><mrow><mi mathvariant="normal">ε</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub><mo>=</mo><mi mathvariant="normal">P</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">y</mi><mi mathvariant="normal"></mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">f</mi><mi mathvariant="normal"></mi><mi mathvariant="normal">f</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal"></mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">e</mi></math></span>&nbsp;== 8.854&nbsp;<span title="Click to copy mathml"><math><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>12</mn></mrow></mrow></msup></math></span>&nbsp;<span title="Click to copy mathml"><math><msup><mrow><mrow><mi>C</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup><msup><mrow><mrow><mi>N</mi></mrow></mrow><mrow><mrow><mo>-</mo><mn>1</mn></mrow></mrow></msup></math></span>&nbsp;<span title="Click to copy mathml"><math><msup><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mo>-</mo><mn>2</mn></mrow></mrow></msup></math></span></p><p>A =&nbsp;<span title="Click to copy mathml"><math><mfrac><mrow><mrow><mi>C</mi><mi>d</mi></mrow></mrow><mrow><mrow><msub><mrow><mrow><mi mathvariant="normal">ε</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub></mrow></mrow></mfrac></math></span>&nbsp;=&nbsp;<span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>2</mn><mi></mi><mo>×</mo><mn>0.5</mn><mi mathvariant="normal"></mi><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>2</mn></mrow></mrow></msup></mrow></mrow><mrow><mrow><mn>8.854</mn><mi mathvariant="normal"></mi><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>12</mn></mrow></mrow></msup></mrow></mrow></mfrac></math></span>&nbsp;= 1129&nbsp;<span title="Click to copy mathml"><math><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>6</mn></mrow></mrow></msup></math></span>&nbsp;m = 1129 km</p><p>To avoid this situation, the capacitance of a capacitor is taken in&nbsp;<span title="Click to copy mathml"><math><mi>μ</mi></math></span>&nbsp;F.</p>

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