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Standard XII

Physics

Potential and Potential Difference

A 10 μF capac...

Question

A $10 μ F$ capacitor is fully charged across a $12 V$ battery. The capacitor is then disconnected from the battery and connected across an initially uncharged capacitor $C$ . The voltage across each capacitor is now $3 V$ . What is the unknown capacitance $C$ (in $μ F$ )?

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Solution

Let us suppose, charge on the capacitor before connecting to another capacitor is $Q$ .

After connecting, suppose that charge $q$ gets transfered. As both capacitors are at the same voltage,

$\frac{q}{C} = \frac{Q - q}{C_{0}}$

$\Rightarrow q (\frac{C + C_{0}}{C C_{0}}) = \frac{Q}{C_{0}}$

$∴ \frac{q}{C} = \frac{Q}{C + C_{0}} = \frac{C_{0} V_{0}}{C + C_{0}}$

$\Rightarrow \frac{10 \times 12}{C + 10} = 3$

$∴ C = 30 μ F$

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A 10 μF capacitor is fully charged across a 12 V battery. The capacitor is then disconnected from the battery and connected across an initially uncharged capacitor C. The voltage across each capacitor is now 3 V. What is the unknown capacitance C (in μF)?

Let us suppose, charge on the capacitor before connecting to another capacitor is Q. After connecting, suppose that charge q gets transfered. As both capacitors are at the same voltage, qC=Q−qC0 ⇒q(C+C0CC0)=QC0 ∴qC=QC+C0=C0V0C+C0 ⇒10×12C+10=3 ∴C=30 μF

A $10 μ F$ capacitor is fully charged across a $12 V$ battery. The capacitor is then disconnected from the battery and connected across an initially uncharged capacitor $C$ . The voltage across each capacitor is now $3 V$ . What is the unknown capacitance $C$ (in $μ F$ )?