SATHEE: electrostatic-potential-and-capacitance Question 32

इलेक्ट्रोस्टैटिक क्षमता और धारिता

Question: Q. 2. A capacitor of unknown capacitance is connected across a battery of $V$ volt. A charge of $360 μ C$ is stored in it. When the potential across the capacitor is reduced by $120 V$ , the charge stored in the capacitor becomes $120 μ C$ . Calculate $V$ and the unknown capacitance. What would have been the charge on the capacitor if the voltage were increased by 120 V? U [Delhi (Comptt.) I 2017]

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Solution:

Ans. Calculation of $V$ and unknown capacitance 2 Calculation of charge when voltage is increased by $120 V$ Capacitance

Also,

$\begin{aligned} C & = \frac{Q_{1}}{V_{1}} C & = \frac{Q_{2}}{V_{2}} and C = \frac{Q_{3}}{V_{3}} \frac{360 μ C}{V} & = \frac{120 μ C}{(V - 120)} \end{aligned}$

So,

$3 V - 360 V = V$

$V = 180 V$

$C = \frac{360 μ V}{180 V} = 2 μ F$

$2 μ F = \frac{Q_{3}}{300}$

$Q_{3} = 600 μ C$

Detailed Answer :

(i) Let the initial yoltage $= V$ volts

Charge stored, $Q_{1} = 360 μ C$

$\begin{matrix} (i) & Q_{1} = C V_{1} = C V \end{matrix}$

Now the changed potential

$\begin{aligned} (ii) & V_{2} = (V - 120) volts & Q_{2} = 120 μ C & Q_{2} = C V_{2} \end{aligned}$

Now divide equation (i) by (ii), we have:

$\begin{aligned} \frac{Q_{1}}{Q_{2}} & = \frac{C V_{1}}{C V_{2}} \frac{360 μ C}{120 μ C} & = \frac{V}{V - 120} \end{aligned}$

On solving, we get $V = 180$ volts

Now value of unknown capacitance $C$ can be calculated as

$\begin{aligned} C & = \frac{Q_{1}}{V} = \frac{360 \times 10^{- 6}}{180} F & = 2 \times 10^{- 6} F = 2 μ F \end{aligned}$

(ii) When the voltage applied increases to $120 V$ , then

$V_{3} = 180 + 120 = 300 V 1 / 2$

Finally the charge stored in the capacitor will be :

$\begin{aligned} Q_{3} & = C V_{3} & = 2 \times 10^{- 6} \times 300 C & = 600 μ C \end{aligned}$

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इलेक्ट्रोस्टैटिक क्षमता और धारिता

Detailed Answer :

विषयसूची

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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