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Electric Charge and Field Physics Electric Charge and Field Physics Class 12th

A capacitor C₁ of capacitance $5 μ F$ is charged to a potential of 30V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor C₂ of capacitance $10 μ F$ as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor C₂ is__________ $μ C .$

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alok kumar singh | Contributor-Level 10

2 months ago

Q = C₁v

...more

Q = C₁v

= 5 × 30

Q = 150 $μ c$

Now it is connected to an unchanged capacitor C₂

Let change on C₁ ® q₁

& 4 C₂ ® q₂

Apply kvL

$\frac{q_{1}}{q} - \frac{q_{2}}{C_{2}} = 0$

Þ q₂ = 2q₁ – (1)

& conservation of change

q₁ + q₂ = 150 – (2)

Þ from (1) & (2)

3q₁ = 150

q₁ = 50 $μ c$

$q_{2} = 100 μ c$

$q_{2} = 100 μ c o n c_{2}$

less

Q = C1v                                                                                                                    = 5 × 30Q = 150  <math> <mrow> <mi>μ</mi> <mi>c</mi> </mrow> </math> Now it is connected to an unchanged capacitor C2Let change on C1 ® q1& 4 C2 ® q2Apply kvL <math> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>q</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>q</mi> </mrow> </mfrac> <mo>−</mo> <mfrac> <mrow> <msub> <mrow> <mi>q</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> </mrow> </math> Þ q2 = 2q1          – (1)                                                & conservation of changeq1 + q2 = 150      – (2)Þ from (1) & (2)3q1 = 150q1 = 50   <math> <mrow> <mi>μ</mi> <mi>c</mi> </mrow> </math> <math> <mrow> <msub> <mrow> <mi>q</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mn>0</mn> <mn>0</mn> <mi>μ</mi> <mi>c</mi> </mrow> </math> <math> <mrow> <msub> <mrow> <mi>q</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mn>0</mn> <mn>0</mn> <mi>μ</mi> <mi>c</mi> <mtext> </mtext> <mtext> </mtext> <mi>o</mi> <mi>n</mi> <mtext> </mtext> <mtext> </mtext> <msub> <mrow> <mi>c</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </math> <div class="photo-widget-full"><div class="figure"><picture><source srcset="" media="(max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1753069310phpHFe6HL.jpeg" alt="" width="213" height="184" loading="lazy"></picture></div><div class="figure"><div class="photo-widget-full"><div class="figure"><picture><source srcset="" media="(max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1753069425phpuiRq2i.jpeg" alt="" width="402" height="295" loading="lazy"></picture></div></div> </div></div>

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