Two capacitors C1=4 μ F and C2=4 μ F in series, are connected in parallel to a third capacitor C 3=4 μ F. This arrangement is then connected to a battery of e.m.f. =4 V, as shown in the figure. How much energy is given by the battery in charging the capacitors?

Question

Two capacitors C1=4 μ F and C2=4 μ F in series, are connected in parallel to a third capacitor C 3=4 μ F. This arrangement is then connected to a battery of e.m.f. =4 V, as shown in the figure. How much energy is given by the battery in charging the capacitors? (A) 96 × 10-6 J (B) 48 × 10-6 J (C) ((32/3)) × 10-6 J (D) ((16/3)) × 10-6 J

Tardigrade Admin · Accepted Answer

C text eq =2+4=6 μ F U text cap =(1/2) C text eq V2=(1/2) ⋅(6 μ) ⋅(4)2=48 μ J U text Battery =2 U text cap =96 μ J

Q. Two capacitors $C_{1} = 4 μ F$ and $C_{2} = 4 μ F$ in series, are connected in parallel to a third capacitor $C_{3} = 4 μ F$ . This arrangement is then connected to a battery of e.m.f. $= 4 V$ , as shown in the figure. How much energy is given by the battery in charging the capacitors?

$96 \times 1 0^{- 6} J$

$48 \times 1 0^{- 6} J$

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

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

$C_{eq} = 2 + 4 = 6 μ F$
$U_{cap} = \frac{1}{2} C_{eq} V^{2} = \frac{1}{2} \cdot (6 μ) \cdot (4)^{2} = 48 μ J$
$U_{Battery} = 2 U_{cap} = 96 μ J$

Q. Two capacitors C1​=4μF and C2​=4μF in series, are connected in parallel to a third capacitor C3​=4μF. This arrangement is then connected to a battery of e.m.f. =4V, as shown in the figure. How much energy is given by the battery in charging the capacitors?

96×10−6J

48×10−6J

(332​)×10−6J

(316​)×10−6J