In the circuit sketched in Fig C1 74 106 F and C2 192 10

In the circuit sketched in Fig., C₁ = 7.4 × 10^-6 F and C₂ = 19.2 × 10^-6 F. What must be the capacitance C_x in microfarads if the ratio V₀/V₁ is to be 36? (V₁ is the voltage across capacitor C₁.) Express the answer with one decimal place.

Solution

as C₁ and C_x are in parallel ,equivalent capacitance is

C₃=C₁+C_x

Voltage across C₃ is

V₁ = V_o*(C₂/C₂+C₃)

=>V_o/V₁ = (C₁+C₂+C_x)/C₂

36 =(7.4*10^-6+19.2*10^-6+C_x)/(19.2*10^-6)

6.912*10^-4 = 26.6*10^-6 +C_x

C_x=6.646*10^-4 C

in uF

C_x =664.6 uF