Answer to Question #184694 in Electric Circuits for Kristine Olar

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

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