Question

Consider the following figure. C - C == (a) Find the equivalent capacitance between points a and for the group of capacitors connected as shown in the figure above. Take C1 - 3.00 WE, C2 - 12.0, and Cy -4.00 UR F (b) What charge is stored on the potential difference between points and bis 60.0V? 9736 Your response differs from the correct answer by more than 10% Double check your calculations. C Need Help? Read

Answer 1

!- Solution : Given, C, = 3 uF = 3x10-6 F C = 12 MF = 12x166 Vah -6 C3 = 4x100 F 60v, - a ci C (a) C3 С2. C2 C₂ C2 -0 C, & C2 are in In the upper portion, series in both left and right side lower portion, the two Cz are parallel. and in in

So C, & C₂ in series is, equivalent of LEGI 1 4+1 5 11 s 12 CIL 12 .. C12 = 12 2.4 MF 5 and equivalent of lower two Cz in parallel is, C 22 C₂ + C₂ - 12 + 12 Cz2 = 24 MF 22 So the circuit becomes, a 2.4 MF 8.8 uf C12 = 2.4u = 24ur (₂2= 24uf T** b b

Now the three capaci upper tors are in parallel. So ste So, c=2.4+ 4+2.4 c = 8.8 MF c & C₂2 are Now this in series. So , equil valent capacitance (Cea) betweeen & b is, a - + i 24 Ceq 8.8 =? Ceqi 8.8 x 24 a 6.44 MF 8.8 +24 64 - [ 60414] F) x

(b) Total charge stored on Ceq Ceq is, Q - Ceq Vab = 6.439 X 60 = 38 6.341 MC of they SO Same .8-8 uf in (potential Q 11 386:34) 8.8 43.902V = C Now as Ceq is series combination 8. 8uf and 24 uf capacitor both have charge. Now ..8.8 MF have voltage difference) of, V = As 8.8 pF is parallel combination of two they all have Same potential. So voltage 3 Ć Charge Q₂ = SV Q₃ 4x 106x 13.902 Q 175.6 uc C12 & so C3 across Vs also 43,902 v. , is isi 0 on C3 = 175.6 MC = =) = ) = w