Two parallel plate capacitors $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$ each having capacitance of $10 \mu \mathrm{~F}$ are individually charged by a 100 V D.C. source. Capacitor $\mathrm{C}_{1}$ is kept connected to the source and a dielectric slab is inserted between it plates. Capacitor $\mathrm{C}_{2}$ is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor $\mathrm{C}_{1}$ is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be ____ V. (Assuming Dielectric constant = 10)

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Capacitance

Two parallel plate capacitors

C_{1}

and

C_{2}

each having capacitance of

10 μ F

are individually charged by a 100 V D.C. source. Capacitor

C_{1}

is kept connected to the source and a dielectric slab is inserted between it plates. Capacitor

C_{2}

is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor

C_{1}

is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be ____ V. (Assuming Dielectric constant = 10)

Answer: 55

Solution

The capacitors start alike, each

10 μ F

charged to

100 V

. For

C_{1}

the slab is slipped in while the battery is still attached, so the voltage is held at

100 V

and the capacitance rises tenfold to

100 μ F

; its charge becomes

100 μ F \times 100 V = 10000 μ C

. For

C_{2}

the battery is removed first, so the charge is frozen at its initial

10 μ F \times 100 V = 1000 μ C

even as the slab raises its capacitance to

100 μ F

. Once both are isolated and joined in parallel, the charges pool and the capacitances add,

\frac{Q _{1} + Q _{2}}{C _{1}^{'} + C _{2}^{'}} = \frac{10000 + 1000}{100 + 100} = \frac{11000}{200}

. The common potential settles at

55 V

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Integer answer

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JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Capacitance

Solution

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