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NEET
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Physics
Chapter
Capacitance

NEET · Physics · Capacitance

A capacitor of capacitance 4 is connected in series with another...

A capacitor of capacitance 4μF4 \mu\text{F} is connected in series with another capacitor of 12μF12 \mu\text{F}. This series combination is connected in parallel with a third capacitor of 5μF5 \mu\text{F}. If the entire arrangement is connected across a 20 V20 \text{ V} battery, what is the charge on the 4μF4 \mu\text{F} capacitor and the total electrostatic energy stored in the circuit, respectively?

Options

  1. A80μC,1.6 mJ80 \mu\text{C}, 1.6 \text{ mJ}
  2. B60μC,3.2 mJ60 \mu\text{C}, 3.2 \text{ mJ}
  3. C60μC,1.6 mJ60 \mu\text{C}, 1.6 \text{ mJ}
  4. D100μC,0.6 mJ100 \mu\text{C}, 0.6 \text{ mJ}

Correct answer

C. 60μC,1.6 mJ60 \mu\text{C}, 1.6 \text{ mJ}

Step-by-step solution

Equivalent capacitance of the series combination of 4μF4 \mu\text{F} and 12μF12 \mu\text{F} is:
Cs=4×124+12=4816=3μFC_s = \dfrac{4 \times 12}{4 + 12} = \dfrac{48}{16} = 3 \mu\text{F}

The charge on the 4μF4 \mu\text{F} capacitor is the same as the charge on this series branch, since capacitors in series carry the same charge.
The voltage across the series combination is the battery voltage, 20 V20 \text{ V}.
Q=Cs×V=3μF×20 V=60μCQ = C_s \times V = 3 \mu\text{F} \times 20 \text{ V} = 60 \mu\text{C}

The total equivalent capacitance of the circuit is the parallel combination of CsC_s and the 5μF5 \mu\text{F} capacitor:
Ceq=3μF+5μF=8μFC_{eq} = 3 \mu\text{F} + 5 \mu\text{F} = 8 \mu\text{F}

The total electrostatic energy stored in the circuit is:
U=12CeqV2=12×(8×10−6 F)×(20 V)2U = \dfrac{1}{2} C_{eq} V^2 = \dfrac{1}{2} \times (8 \times 10^{-6} \text{ F}) \times (20 \text{ V})^2
U=4×10−6×400=1600×10−6 J=1.6 mJU = 4 \times 10^{-6} \times 400 = 1600 \times 10^{-6} \text{ J} = 1.6 \text{ mJ}

Answer: 60μC,1.6 mJ60 \mu\text{C}, 1.6 \text{ mJ}
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