Question

Calculate the energy stored in the capacitor network in the figure below when the capacitors are fully charged and when the capacitances are C1-12 0µF C2=2.0μF, and C3=4 0µF, respectively.

VT=12.0 V

Answer 1

Let us find voltage through each capacitor.

C2 and C3 are in parallel, so voltage across C2 and C3 will be the same.

C1 = 12 µF

C2 + C3 = 6 µF

$V_1 = 12 \times \frac{6}{6+12} = 4 \;V$

V2 = V3 = 12 – 4 = 8 V

Energy $= \frac{1}{2}CV^2$

$U_1 = \frac{1}{2}(12)(4)^2 = 96 \;µJ \\ U_2 = \frac{1}{2}(2)(8)^2 = 64 \;µJ \\ U_3 = \frac{1}{2}(4)(8)^2 = 128 \;µJ$