Capacitors and are connected in parallel

PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance

Problem

Capacitors

C_1=10\,\mu\text{F}

and

C_2=20\,\mu\text{F}

are connected in parallel. This parallel combination is connected in series with a capacitor

C_3=5\,\mu\text{F}

across a

30\,\text{V}

ideal battery. After the capacitors are fully charged, the battery is disconnected from the circuit without discharging the capacitors. A dielectric slab of dielectric constant

\kappa = 2

is then completely inserted between the plates of

C_3

, fully filling the gap. (i) Calculate the charge on each capacitor immediately before the battery is disconnected. (ii) Determine the new value of the capacitance of

C_3

after the dielectric is inserted. (iii) Find the new potential difference across

C_3

and the common potential difference across the parallel branch containing

C_1

and

C_2

." (iv) Compute the total energy stored in the system (a) before and (b) after the insertion of the dielectric. Hence determine the change in energy of the system.

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