In the figure C_1 = 10pF, C_2 = 20pF, C_3 = 30pF, C_4 = 40pF, the potential of t

Question

In the figure C_1 = 10pF, C_2 = 20pF, C_3 = 30pF, C_4 = 40pF, the potential of the battery is 50 volts. By the way, pF is 10^-15 Farads Solve for the value of the equivalent capacitance of the circuit, reducing the diagram to include only the battery and one equivalent capacitor. What is the total charge stored in the circuit? What is the total Potential energy stored in the circuit? Variable capacitors have a fixed cross-sectional area, but contain a screw mechanism that allows you to vary the plate separation distance. You purchase a variable capacitor to use as the Equivalent Capacitor for this system. The cross-sectional area of the variable capacitor is 0.025 cm^2. What should be the plate-to-plate separation distance of the variable capacitor so that the capacitance matches your answer from part a?

Explanation / Answer

here C1 and C2 in parallel

C12 = C1 + C2 = 30 pF

similalry C3 and C4 in parallel

C34 = C3 + C4 = 70 pF

now C12 and C34 in series

Ceq = C12*C34/(C12+C34)

Ceq = 21 pF

part b )

Q = Ceq*V = 1.05 x 10^-12 C = 1050 pC

part c )

U = Ceq*V^2/2

U = 2.625 x 10^-11 J

part d )

C = eo*A/d

d = eo*A/C

A = 0.025 cm^2 = 0.025 x 10^-4 m^2

C = 21 x 10^-15 F

eo = 8.85 x 10^-12

d = 1.05 x 10^-3 m

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