A 5 $\mu$F capacitor is charged fully by a 220 V supply. It is then disconnected from the supply and is connected in series to another uncharged 2.5 $\mu$F capacitor. If the energy change during the charge redistribution is ${X \over {100}}J$ then value of X to the nearest integer is _____.
Answer (integer)
4
Solution
u<sub>i</sub> = $\frac{1}{2}$ $\times$ 5 $\times$ 10<sup>-6</sup>$\times$220
<br><br>Final common potential
<br><br>= $\frac{220\times 5+0\times 2.5}{5+2.5}$ = 220 $\times$ $\frac{2}{3}$
<br><br>u<sub>f</sub> = $\frac{1}{2}$ $\times$ (5 + 2.5)$\times$10<sup>-6</sup> $\times$ $\left( 220\times \frac{2}{3} \right)^{2}$
<br><br>$\Delta$u = u<sub>i</sub> - u<sub>f</sub>
<br><br>$\Rightarrow$ $\Delta$u = –403.33 × 10<sup>–4</sup>
<br><br>$\Rightarrow$ –403.33 × 10<sup>–4</sup> = ${X \over {100}}J$
<br><br>$\Rightarrow$ X = -4.03
<br><br>Value of X is approximate 4
About this question
Subject: Physics · Chapter: Electrostatics · Topic: Electric Potential and Capacitance
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