For the circuit shown in the figure below, the capacitors were each discharged b

Question

For the circuit shown in the figure below, the capacitors were each discharged before being connected to the voltage source V = 216 V. 4.0 F 12.0H 15.0 F (a) Find the equlvalent capacitance of the combination 15.158 (b) Find the charge stored on the positively charged plate of each capacitor. 15.0 F capacitor 4.0 F capacitor 12.0 F capacitor (c) Find the voltage across each capacitor 15.0 F capacitor 4.0 F capacitor 12.0 F capacitor [d) Find the energy stored in each capacitor. 15.0 pF capacitor | 4.0 F capacitor 12.0 F capacitor mJ m] eBook

Explanation / Answer

(a) 5uF and 15 uF are in series.

C1 = 4 x 15 / (4 + 15) = 3.16 uF

now C1 and 12uF are in parallel,

Ceq = C1 + 12 = 15.16 uF

(b) C1 and 12uF are connected in parallel with V.

voltage across C1 = 216 Volt

charge = C1 V =216 x 3.16 = 686.6 uC

charge on 15uF = charge on 4uF = 686.6 uC

charge on 12uF = 12 x 216 = 2592 uC

(c) acrss 15uF = (686.6/15) = 45 Volt

across 4uf = 686.6 / 4 = 171volt

across 12uF = 216 Volt

(d) energy in 15uF = (15 x 10^-6)(45^2)/2 = 0.0152 J

= 15.2 mJ

energy in 4uF = (4 x 10^-6)(171)^2 /2 = 0.0584 J

= 58.4 mJ

energy in 12uF = (12 x 10^-6)(216^2) / 2

= 0.28 J

= 280 mJ

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