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Physics-

General

Easy

Question

Two capacitors $C subscript 1 end subscript equals 2 mu F$ and $C subscript 2 end subscript equals 6 mu F$ in series, are connected in parallel to a third capacitor $C subscript 3 end subscript equals 4 mu F$ . This arrangement is then connected to a battery of e.m.f. = 2V, as shown in the figure. How much energy is lost by the battery in charging the capacitors

$22 \times 1 0^{- 6} J$
$11 \times 1 0^{- 6} J$
$(\frac{32}{3}) \times 1 0^{- 6} J$
$(\frac{16}{3}) \times 1 0^{- 6} J$

The correct answer is: $11 cross times 1 0 to the power of negative 6 end exponent J$

$C subscript e q end subscript equals fraction numerator C subscript 1 end subscript C subscript 2 end subscript over denominator C subscript 1 end subscript plus C subscript 2 end subscript end fraction plus C subscript 3 end subscript equals fraction numerator 2 cross times 6 over denominator 2 plus 6 end fraction plus 4 equals 5.5 mu F$
Energy supplied $left parenthesis E right parenthesis equals Q V equals C V to the power of 2 end exponent equals 22 cross times 1 0 to the power of negative 6 end exponent J$
P.E. stored $left parenthesis U right parenthesis equals fraction numerator 1 over denominator 2 end fraction C subscript e q end subscript V to the power of 2 end exponent equals fraction numerator 1 over denominator 2 end fraction cross times 5.5 cross times left parenthesis 2 right parenthesis to the power of 2 end exponent equals 11 cross times 1 0 to the power of negative 6 end exponent J$
Þ Energy lost $equals E minus U equals 11 cross times 1 0 to the power of negative 6 end exponent J$

Related Questions to study

The combination of capacitors with $C subscript 1 end subscript equals 3 mu F comma C subscript 2 end subscript equals 4 mu F$ and $C subscript 3 end subscript equals 2 mu F$ is charged by connecting AB to a battery. Consider the following statements
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II. Charge on C₁ = Charge on C₂ + Charge on C₃
III. Potential drop across C₁ = Potential drop across C₂ = Potential drop across C₃
Which of these is/are correct

The combination of capacitors with $C subscript 1 end subscript equals 3 mu F comma C subscript 2 end subscript equals 4 mu F$ and $C subscript 3 end subscript equals 2 mu F$ is charged by connecting AB to a battery. Consider the following statements
I. Energy stored in $C subscript 1 end subscript$ = Energy stored in $C subscript 2 end subscript$ + Energy stored in $C subscript 3 end subscript$
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III. Potential drop across C₁ = Potential drop across C₂ = Potential drop across C₃
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