Question

Assume you are given two resistors with resistances R =8.0 kN and R2-4,0 kN and two capacitors with capacitances C,=8.0 pF and C=4.0 PF. a) Calculate the equivalent resistances Reg and the equivalent capacitance Ceq if the resistors are connected in series and the capacitors are connected in parallel. b) Now, use the Reg and Ce that you calculate in part (a) to construct an RC circuit. An emf of 27 V is applied across Reg and Ceg to charge the capacitor. After Ceq is fully charged, the battery is removed at t=0. Calculate the charge on the Ceq after t= 12 ps. c) If the resistor R, is made of iron wire with radius R= 3 mm, calculate the length of this wire. The resistivity of iron is Piron = 9.68x10.m. d) If the capacitance C, has square parallel-plates with the area A = 20 cm?. Calculate the separation between plates. -8

Answer 1

Two resistances Ri= 8. okr. R₂-4.0KR and two Capacitors Go 8 out (2 4.0 uf Reg when R, and R₂ in Series In serie circuit current will be hame in earch component Vtotal & I Reg= IR TIR2 Reg. R, + R2 Vitz Req= 8.0 +4.0= 12.0kr a and Ca in parallel, voltage Ceg when will will be same so Cegra Cut CV Ceq = Citra Ceq = 8+4= 12.04f

her (6) Coq let & vosinut Vo = aty emf After fully charge of capacitor o dd TIR di Q=cv At Req Ceq t-o + alca At any intant IR+ or - o where - Ceq Vo at to Roda because at to at cey is fully chargede solving this first order differentiate equation -t/Regler get = cavo Now on charge Coq at t= 12us g= - 12418 Ceq Vo e 12x12 yifxk2 12 x 10 x 27 x exp(- Teater) Q= 323. 97 MF, at t=12 ous

we Know that resistance in a wire given R = se A Неде R= 8.0KR f = 9.68x108 em radius= 3mm Area A=T8²= A ( 3x10 3 ) 2 = 2.82x10 5² put these data into above è equ 8x103 = 9.68x108 xe 2.32 x los = 23.30x105m d) know Capacitance between bo parallel plate 1 Plate Area (= EA d at A tttttttttttt d Now d - EOA С, Es = 8.354 8 10 12 f/m - 8.854 x 10 12 x 20x104 4x106 d = 44.27 x 1000m