Two capacitors of capacitance C1=2 μF and C2=3 μF are connected as shown, to two batteries A and

step 1 In this question, you have to find the energy stored in the capacitors, the two capacitors, the

Two capacitors of capacitance C1=2 μF and C2=3 μF are...

Two capacitors of capacitance $C_{1}=2 \mu \mathrm{F}$ and $C_{2}=3 \mu \mathrm{F}$ are connected as shown, to two batteries $A$ and $B$ which have $\mathrm{emf} 6 \mathrm{~V}$ and $10 \mathrm{~V}$ respectively. Energies stored in the capacitors $C_{1}$ and $C_{2}$ are (a) $36 \mu \mathrm{J}, 36 \mu \mathrm{J}$ (b) $24 \mu \mathrm{J}, 24 \mu \mathrm{J}$ (c) $24 \mu \mathrm{J}, 36 \mu \mathrm{J}$ (d) $36 \mu \mathrm{J}, 24 \mu \mathrm{J}$

Two capacitors of capacitance $C_{1}=2 \mu \mathrm{F}$ and $C_{2}=3 \mu \mathrm{F}$ are connected as shown, to two batteries $A$ and $B$ which have $\mathrm{emf} 6 \mathrm{~V}$ and $10 \mathrm{~V}$ respectively. Energies stored in the capacitors $C_{1}$ and $C_{2}$ are
(a) $36 \mu \mathrm{J}, 36 \mu \mathrm{J}$
(b) $24 \mu \mathrm{J}, 24 \mu \mathrm{J}$
(c) $24 \mu \mathrm{J}, 36 \mu \mathrm{J}$
(d) $36 \mu \mathrm{J}, 24 \mu \mathrm{J}$

Key Concepts

Capacitor

A capacitor is an electronic component that stores energy in an electric field between its conductors. Its ability to hold charge is expressed by its capacitance, measured in farads, and it plays a key role in controlling voltage and power in circuits.

Energy Stored in a Capacitor

The energy stored in a capacitor is determined by the formula E = ½CV², where E is the energy, C is the capacitance, and V is the voltage across the capacitor. This relationship is fundamental in analyzing how much energy is maintained in capacitors operating at a given voltage.

DC Circuit Analysis

Analyzing circuits that include capacitors and batteries requires understanding DC circuit principles such as Kirchhoff’s Voltage Law, which ensures that the sum of voltages around any closed loop equals zero, and the idea of voltage division. This helps determine the distribution of voltage across various components in the circuit.

Series and Parallel Capacitor Configurations

The configuration of capacitors in a circuit—whether connected in series or parallel—affects both the overall equivalent capacitance and the voltage across each capacitor. In a parallel configuration, all capacitors share the same voltage, while in a series configuration, they share the same charge, necessitating different approaches for calculating their energy storage and effective capacitance.

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