physics-class-12-unit-02-chapter-01-cylindrical-spherical-capacitors-series-parallel-combin-l1-9-bdszgl-ii0e

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxcylindrical-spherical-capacitors-series-and-parallel-combinationprimary"><primary style="font-size:24px;">Cylindrical Spherical Capacitors Series and Parallel Combination</primary></h3>
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<div style='float: left; width:100%;'>
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<div style='float: right; width:0%;'>
<p><img alt="image" src="https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-12-unit-02-chapter-01-cylindrical-spherical-capacitors-series-parallel-combin-l1_9-bdszgl-ii0e-014-0027.6.jpg"></p>
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<footer style = "font-size: 18px">  $\rightarrow$  $\rightarrow$ <span style = "color:blue"> Cylindrical Spherical Capacitors Series and Parallel Combination </span> $\rightarrow$ Parallel Plate Capacitor $\rightarrow$ Cylindrical Capacitor </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-1"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxparallel-plate-capacitorprimary"><primary style="font-size:24px;">Parallel Plate Capacitor</primary></h3>
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<div style='float: left; width:50%;text-align:left; font-size:30px; '>
<ul>
<li>
<p>Consists of two plates of area A separated by distance d.</p>
</li>
<li>
<p>Between these two plates there is an electric field.</p>
</li>
<li>
<p>$\epsilon_0$ is the permittivity of free space.</p>
</li>
<li>
<p>C =  $\frac{\epsilon_0 A}{d}$</p>
</li>
</ul>
<ul>
<li>
<p>Unit of capacitance : FARAD</p>
</li>
<li>
<p>C = $\frac{Q}{V}$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%;'>
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<footer style = "font-size: 18px">  $\rightarrow$ Cylindrical Spherical Capacitors Series and Parallel Combination $\rightarrow$ <span style = "color:blue"> Parallel Plate Capacitor </span> $\rightarrow$ Cylindrical Capacitor $\rightarrow$ Potential Difference </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-2"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxcylindrical-capacitorprimary"><primary style="font-size:24px;">Cylindrical Capacitor</primary></h3>
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<div style='float: left; width:50%;text-align:left;font-size:30px'>
<ul>
<li>
<p>$\lambda$ is the charge per unit length.</p>
</li>
<li>
<p>There is no Gaussian flux, electric flux on the top and bottom surface of the cylinder of the Gaussian surface, there is only flux from the cylindrical surface</p>
</li>
<li>
<p>$2 \pi r \cdot l \cdot E  =\frac{\lambda l}{\epsilon_0}$</p>
</li>
<li>
<p>$\vec{E}  =\frac{\lambda}{2 \pi \epsilon_0 r} \hat{r}$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/7f0b96b9-1621-48be-1982-7143ff044400/public"  width="70%" >

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<footer style = "font-size: 18px"> Cylindrical Spherical Capacitors Series and Parallel Combination $\rightarrow$ Parallel Plate Capacitor $\rightarrow$ <span style = "color:blue"> Cylindrical Capacitor </span> $\rightarrow$ Potential Difference $\rightarrow$ Capacitance </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-3"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxpotential-differenceprimary"><primary style="font-size:24px;">Potential Difference</primary></h3>
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<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$V  =V(a)-V(b)$</p>
</li>
<li>
<p>$ =-\int_b^a \vec{E} \cdot d \vec{r}$ $=\frac{\lambda}{2 \pi \epsilon_0} \int_a^b \frac{d r}{r}$</p>
</li>
<li>
<p>$V=\frac{\lambda}{2 \pi \epsilon_0} \ln \left(\frac{b}{a}\right)$</p>
</li>
</ul>
<ul>
<li>Length L : charge Q=$\lambda$L</li>
</ul>
</div>
<div style='float: right; width:0%; max-width:400px;'>
<p><img alt="image" src="https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-12-unit-02-chapter-01-cylindrical-spherical-capacitors-series-parallel-combin-l1_9-bdszgl-ii0e-0003.jpg"></p>
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<footer style = "font-size: 18px"> Parallel Plate Capacitor $\rightarrow$ Cylindrical Capacitor $\rightarrow$ <span style = "color:blue"> Potential Difference </span> $\rightarrow$ Capacitance $\rightarrow$ Coaxial Cables </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-4"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxcapacitanceprimary"><primary style="font-size:24px;">Capacitance</primary></h3>
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<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$ V=\frac{Q}{2 \pi \epsilon_0 L} \ln \left(\frac{b}{a}\right)$</p>
</li>
<li>
<p>$V=\frac{Q}{C}$</p>
</li>
<li>
<p>Capacitance C = $\frac{2 \pi \epsilon_0 L}{\ln (b / a)}$</p>
</li>
<li>
<p>Capacitance per unit length = $\frac{C}{L}=\frac{2 \pi \epsilon_0}{\ln (b / a)}$</p>
</li>
</ul>
</div>
<div style='float: right; width:0%; max-width:400px;'>
<p><img alt="image" src="https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-12-unit-02-chapter-01-cylindrical-spherical-capacitors-series-parallel-combin-l1_9-bdszgl-ii0e-0004.jpg"></p>
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<footer style = "font-size: 18px"> Cylindrical Capacitor $\rightarrow$ Potential Difference $\rightarrow$ <span style = "color:blue"> Capacitance </span> $\rightarrow$ Coaxial Cables $\rightarrow$ Spherical Capacitor </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-5"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxcoaxial-cablesprimary"><primary style="font-size:24px;">Coaxial Cables</primary></h3>
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<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<p><strong>Example</strong></p>
<ul>
<li>
<p>a = 2mm</p>
</li>
<li>
<p>b = 4mm</p>
</li>
<li>
<p>C = $\frac{2 \pi \epsilon_o}{\ln (b / a)}=\frac{2 \pi \times 8.85 \times 10^{-12}}{\ln (4 / 2)}$</p>
</li>
</ul>
<ul>
<li>$\simeq 80 \mathrm{pF} / \mathrm{m}=80 \times 10^{-12} \mathrm{F} / \mathrm{m}$</li>
</ul>
<ul>
<li>Coaxial cables  $C \sim 70$ pf/m</li>
</ul>
</div>
<div style='float: right; width:0%; max-width:400px;'>
<p><img alt="image" src="https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-12-unit-02-chapter-01-cylindrical-spherical-capacitors-series-parallel-combin-l1_9-bdszgl-ii0e-0005.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Potential Difference $\rightarrow$ Capacitance $\rightarrow$ <span style = "color:blue"> Coaxial Cables </span> $\rightarrow$ Spherical Capacitor $\rightarrow$ Potential Difference </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-6"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxspherical-capacitorprimary"><primary style="font-size:24px;">Spherical Capacitor</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>The inner sphere is charged positively, assume to be charged positively the outer sphere is assumed to be charged negatively</li>
</ul>
<ul>
<li>Radius of inner sphere = $\ r_a$</li>
<li>Radius of outer sphere = $\ r_b$</li>
<li>Electric Flux  = $4 \pi r^2 $E</li>
</ul>
<ul>
<li>
<p>$4 \pi r^2 $E = $\frac{Q}{\epsilon_0}$</p>
</li>
<li>
<p>$\vec E = \frac{Q}{4 \pi \epsilon_0 r^2} \hat{r}$</p>
</li>
</ul>
</div>
<div style='float: right; width:50%; max-width:400px;'>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/1521a539-4dc0-46af-c73e-9c7cf5caaf00/public"  width="50%" >

</main>
<hr>
<footer style = "font-size: 18px"> Capacitance $\rightarrow$ Coaxial Cables $\rightarrow$ <span style = "color:blue"> Spherical Capacitor </span> $\rightarrow$ Potential Difference $\rightarrow$ Capacitance </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-7"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxpotential-differenceprimary-1"><primary style="font-size:24px;">Potential Difference</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$V  =-\int_{r_b}^{r_a} \vec{E} \cdot d \vec{r}$$=\int_{r_a}^{r_b} \frac{d}{4 \pi \epsilon_o r^2} d r$</p>
</li>
<li>
<p>$=\frac{Q}{4 \pi \epsilon_0}\left(-\frac{1}{r}\right)_{r_a}^{r_b}$</p>
</li>
<li>
<p>$=\frac{Q}{4 \pi \epsilon_0}\left(\frac{1}{r_a}-\frac{1}{r_b}\right)$</p>
</li>
<li>
<p>$V  =\frac{Q}{4 \pi \epsilon_0} \frac{\left(r_b-r_a\right)}{r_a r_b}$</p>
</li>
</ul>
</div>
<div style='float: right; width:0%; max-width:400px;'>
<p><img alt="image" src="https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-12-unit-02-chapter-01-cylindrical-spherical-capacitors-series-parallel-combin-l1_9-bdszgl-ii0e-0007.jpg"></p>
</main>
<hr>
<footer style = "font-size: 18px"> Coaxial Cables $\rightarrow$ Spherical Capacitor $\rightarrow$ <span style = "color:blue"> Potential Difference </span> $\rightarrow$ Capacitance $\rightarrow$ Capacitance </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-8"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxcapacitanceprimary-1"><primary style="font-size:24px;">Capacitance</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left; font-size:30px;'>
<ul>
<li>
<p>Q is the charge carried by the conductors</p>
</li>
<li>
<p>C = $\frac{Q}{V}$= $\frac{4 \pi \epsilon_0\left(r_a r_b\right)}{\left(r_b-r_a\right)}$</p>
</li>
<li>
<p>Both conductors carry the same amount of charge Q</p>
</li>
</ul>
</div>
<div style='float: right; width:0%; max-width:400px; '>
<p><img alt="image" src="https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-12-unit-02-chapter-01-cylindrical-spherical-capacitors-series-parallel-combin-l1_9-bdszgl-ii0e-0008.jpg"></p>
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<hr>
<footer style = "font-size: 18px"> Spherical Capacitor $\rightarrow$ Potential Difference $\rightarrow$ <span style = "color:blue"> Capacitance </span> $\rightarrow$ Capacitance $\rightarrow$ Spherical Capacitor </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-9"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxcapacitanceprimary-2"><primary style="font-size:24px;">Capacitance</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>Capacitance of a single sphere conducting sphere of radius r a.</p>
</li>
<li>
<p>The other conductor which is supposed to be carrying negative charges as infinite size</p>
</li>
<li>
<p>Limit  $r_b \rightarrow \infty$</p>
</li>
<li>
<p>C = $4 \pi \epsilon_o r_a$</p>
</li>
</ul>
</div>
<div style='float: right; width:0%; max-width:400px; '>
<p><img alt="image" src="https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-12-unit-02-chapter-01-cylindrical-spherical-capacitors-series-parallel-combin-l1_9-bdszgl-ii0e-0008.jpg"></p>
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<hr>
<footer style = "font-size: 18px"> Potential Difference $\rightarrow$ Capacitance $\rightarrow$ <span style = "color:blue"> Capacitance </span> $\rightarrow$ Spherical Capacitor $\rightarrow$ Capacitance of The Earth </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-10"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxspherical-capacitorprimary-1"><primary style="font-size:24px;">Spherical Capacitor</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$r_a$ = 1mm, $r_b = \infty$</p>
</li>
<li>
<p>C= $4 \pi \epsilon_0 r_a$</p>
</li>
<li>
<p>= $\frac{10^{-3}}{9 \times 10^9} \simeq 0.11 \mathrm{pF}=0.11 \times 10^{-12} \mathrm{F}$</p>
</li>
<li>
<p>If I put a charge of 1 pC then the voltage generated.</p>
</li>
<li>
<p>$V=\frac{Q}{C}=\frac{10^{-12}}{0.11 \times 10^{-12}} \approx 9 \mathrm{V}$</p>
</li>
</ul>
</div>
<div style='float: right; width:0%; max-width:400px;'>
<p><img alt="image" src="https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-12-unit-02-chapter-01-cylindrical-spherical-capacitors-series-parallel-combin-l1_9-bdszgl-ii0e-0009.jpg"></p>
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<footer style = "font-size: 18px"> Capacitance $\rightarrow$ Capacitance $\rightarrow$ <span style = "color:blue"> Spherical Capacitor </span> $\rightarrow$ Capacitance of The Earth $\rightarrow$ Capacitors Connected in Series </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-11"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxcapacitance-of-the-earthprimary"><primary style="font-size:24px;">Capacitance of The Earth</primary></h3>
<hr>
<main>
<div style='float: left; width:100%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>Assume the earth to be spherical</p>
</li>
<li>
<p>R = 6371 km</p>
</li>
<li>
<p>$C  = 4 \pi \epsilon_0 \cdot R$ $=\frac{6.371 \times 10^6}{9 \times 10^9}$</p>
</li>
<li>
<p>$\simeq 7.08 \times 10^{-4} \mathrm{F}$ $=708 \mu \mathrm{F}$</p>
</li>
</ul>
</div>
<div style='float: right; width:0%; max-width:400px; '>
<p><img alt="image" src="https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-12-unit-02-chapter-01-cylindrical-spherical-capacitors-series-parallel-combin-l1_9-bdszgl-ii0e-00010.jpg"></p>
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<hr>
<footer style = "font-size: 18px"> Capacitance $\rightarrow$ Spherical Capacitor $\rightarrow$ <span style = "color:blue"> Capacitance of The Earth </span> $\rightarrow$ Capacitors Connected in Series $\rightarrow$ Capacitors Connected in Series </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-12"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxcapacitors-connected-in-seriesprimary"><primary style="font-size:24px;">Capacitors Connected in Series</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>They are not connected to any other part of the circuit. So, the net charge within this must be equal to 0</p>
</li>
<li>
<p>$V=V_1+V_2+V_3$</p>
</li>
<li>
<p>Charge supplied  = q</p>
</li>
<li>
<p>$V_1=\frac{q}{C_1} ; \quad V_2=\frac{q_1}{C_2} ; \quad V_3=\frac{q}{C_3}$</p>
</li>
</ul>
</div>
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<footer style = "font-size: 18px"> Spherical Capacitor $\rightarrow$ Capacitance of The Earth $\rightarrow$ <span style = "color:blue"> Capacitors Connected in Series </span> $\rightarrow$ Capacitors Connected in Series $\rightarrow$ Capacitances in Parallel </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-13"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxcapacitors-connected-in-seriesprimary-1"><primary style="font-size:24px;">Capacitors Connected in Series</primary></h3>
<hr>
<main>
<div style='float: left; width:70%;text-align:left;font-size:30px'>
<ul>
<li>
<p>$V=V_1+V_2+V_3$ $ = \frac{q}{C_1} + \frac{q}{C_2} + \frac{q}{C_3}$</p>
</li>
<li>
<p>$C = \frac{q}{V}$</p>
</li>
<li>
<p>$\frac{V}{q}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}$</p>
</li>
<li>
<p>$\frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}$</p>
</li>
</ul>
<p><span style="color:blue">n Capacitor connected in series.</span></p>
<ul>
<li>$ \frac{1}{C}  =\sum_{i=1}^{N} \frac{1}{C_i}$ $=\frac{1}{C_1}+\frac{1}{C_2}+\cdots+\frac{1}{C_n}$</li>
</ul>
</div>
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<footer style = "font-size: 18px"> Capacitance of The Earth $\rightarrow$ Capacitors Connected in Series $\rightarrow$ <span style = "color:blue"> Capacitors Connected in Series </span> $\rightarrow$ Capacitances in Parallel $\rightarrow$ Capacitances in Parallel </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-14"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxcapacitances-in-parallelprimary"><primary style="font-size:24px;">Capacitances in Parallel</primary></h3>
<hr>
<main>
<div style='float: left; width:60%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>Capacitor have a potential difference of V</p>
</li>
<li>
<p>Charge on $C_1 = q_1$</p>
</li>
<li>
<p>Charge on $C_2 = q_2$</p>
</li>
<li>
<p>Charge on $C_3 = q_3$</p>
</li>
</ul>
</div>
<div style='float: right; width:40%; max-width:400px; '>
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<footer style = "font-size: 18px"> Capacitors Connected in Series $\rightarrow$ Capacitors Connected in Series $\rightarrow$ <span style = "color:blue"> Capacitances in Parallel </span> $\rightarrow$ Capacitances in Parallel $\rightarrow$ Capacitances in Parallel </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-15"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
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<div style='float: left; width:50%; text-align:left; font-size: 30px'>
<p><strong>Total Charge Supplied</strong></p>
<ul>
<li>
<p>$q = q_1 + q_2 + q_3$</p>
</li>
<li>
<p>$q_1 = C_1V , q_2 = C_2V  , q_3 = q_3V$</p>
</li>
<li>
<p>$q =(C_1+C_2+C_3)V$</p>
</li>
<li>
<p>$C = \frac{q}{V}$</p>
</li>
</ul>
</div>
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<footer style = "font-size: 18px"> Capacitors Connected in Series $\rightarrow$ Capacitances in Parallel $\rightarrow$ <span style = "color:blue"> Capacitances in Parallel </span> $\rightarrow$ Capacitances in Parallel $\rightarrow$ Capacitances in Parallel </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-16"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxcapacitances-in-parallelprimary-2"><primary style="font-size:24px;">Capacitances in Parallel</primary></h3>
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<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>$C = C_1 + C_2 + C_3$</li>
</ul>
<p><span style="color:blue">For n capacitor in parallel.</span></p>
<ul>
<li>$C=\sum_{i=1}^n C_i$</li>
</ul>
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<footer style = "font-size: 18px"> Capacitances in Parallel $\rightarrow$ Capacitances in Parallel $\rightarrow$ <span style = "color:blue"> Capacitances in Parallel </span> $\rightarrow$ Capacitances in Parallel $\rightarrow$ Problem </footer>

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<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>For example:</p>
</li>
<li>
<p>$C=\sum_{i=1}^n C_i$</p>
</li>
<li>
<p>$C = 10 + 2 = 12 \mu F$</p>
</li>
</ul>
</div>
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<footer style = "font-size: 18px"> Capacitances in Parallel $\rightarrow$ Capacitances in Parallel $\rightarrow$ <span style = "color:blue"> Capacitances in Parallel </span> $\rightarrow$ Problem $\rightarrow$ Problem </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-18"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxproblemprimary"><primary style="font-size:24px;">Problem</primary></h3>
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<div style='float: left; width:70%;text-align:left;font-size:30px;'>
<p><strong>Example</strong></p>
<ul>
<li>
<p>$C_\text{23} = C_2 +C_3$</p>
</li>
<li>
<p>$ C \Rightarrow$</p>
</li>
<li>
<p>$\frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2+C_3}$</p>
</li>
<li>
<p>$C_1=25 \mu \mathrm{f}, \quad C_2=5 \mu \mathrm{f},$</p>
</li>
<li>
<p>$C_{23}=C_2+C_3=25 \mu \mathrm{F}$</p>
</li>
</ul>
</div>
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<footer style = "font-size: 18px"> Capacitances in Parallel $\rightarrow$ Capacitances in Parallel $\rightarrow$ <span style = "color:blue"> Problem </span> $\rightarrow$ Problem $\rightarrow$ Problem </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-19"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxproblemprimary-1"><primary style="font-size:24px;">Problem</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$C_\text{23} = C_2 +C_3$</p>
</li>
<li>
<p>$\frac{1}{C} =\frac{1}{C_1}+\frac{1}{C_{23}}$ $ =\frac{1}{25}+\frac{1}{25}$ $=\frac{2}{25}$</p>
</li>
<li>
<p>$C =\frac{25}{2}=12.5 \mu \mathrm{F}$</p>
</li>
</ul>
</div>
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<footer style = "font-size: 18px"> Capacitances in Parallel $\rightarrow$ Problem $\rightarrow$ <span style = "color:blue"> Problem </span> $\rightarrow$ Problem $\rightarrow$ Problem </footer>

<h3 id="success-stylefont-size25px-cylindrical-spherical-capacitors-series-parallel-combination-l-1success-20"><Success style="font-size:25px;"> Cylindrical-Spherical-Capacitors-Series-Parallel-Combination L-1</Success></h3>
<h3 id="primary-stylefont-size24pxproblemprimary-2"><primary style="font-size:24px;">Problem</primary></h3>
<hr>
<main>
<div style='float: left; width:70%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>$V = 10V$</p>
</li>
<li>
<p>$q=CV=12.5 \times 10^{-6} \times 10 \mathrm{V}=125 \mu \mathrm{c}$</p>
</li>
<li>
<p>$V_1=\frac{q}{C_1}=\frac{125 \times 10^{-6}}{25 \times 10^{-6}}=5 \mathrm{V}$</p>
</li>
<li>
<p>$q_2=C_2 V=5 \times 10^{-6} \times 5=25 \mu C$</p>
</li>
<li>
<p>$q_3=C_3 V=20 \times 10^{-6} \times 5=100 \mu C$</p>
</li>
<li>
<p>We can use the law for adding capacitors connected in series or in parallel and find the equivalent capacitor.</p>
</li>
</ul>
</div>
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<footer style = "font-size: 18px"> Problem $\rightarrow$ Problem $\rightarrow$ <span style = "color:blue"> Problem </span> $\rightarrow$ Problem $\rightarrow$ Thankyou </footer>

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<h3 id="primary-stylefont-size24pxproblemprimary-3"><primary style="font-size:24px;">Problem</primary></h3>
<hr>
<main>
<div style='float: left; width:50%;text-align:left;font-size:30px;'>
<ul>
<li>
<p>Consider a parallel plate capacitor as shown:</p>
</li>
<li>
<p>You have two conducting plates separated by distance d.</p>
</li>
<li>
<p>A solid metallic slab of thickness $\frac{d}{2}$ is inserted between the two plates without touching them. what is on Capacitance before insertion & after insertion.</p>
</li>
</ul>
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<footer style = "font-size: 18px"> Problem $\rightarrow$ Problem $\rightarrow$ <span style = "color:blue"> Problem </span> $\rightarrow$ Thankyou $\rightarrow$ </footer>