Question

Switch S shown in the figure below has been closed for a long time, and the electric circuit carries a constant current. Take C 3.00 F, C2 6.00 uF, R1 = 4.00 k, and R2 = 7.00 k. The power delivered to R2 is 2.00 W. R C - S R, (a) Find the charge on C. Q 222.18 Your response is within 10 % of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. C (b) Now the switch opened. After many milliseconds, by how much has the charge on C2 changed? 444.36 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. uC

Answer 1

Solution :- Given, C,= 3pF = 3x10 of C = 6uf = 6x100F R, = 4 kr = 4x10² R2 = 7 ks = 7x10?? Power in R₂, P2=2w when switch s is closed for long time, both capacitors will get fully charged and does not allow any current Horough them (ie C, & (2). So the new circuit becomes, TI ZI v+

Let the current flowing in R, & R2 he current lowing in is So I. Power in R₂ , P2 = 1/R => I'R, = 2 = I x7X10% = 2 => I'= 20 = {x103 »» Is War 103 = 0.0169 A This is the current through both R and R2. So voltage across R., and Rz is, Y = IR, = 0.0169X 4x103 | Van = 67.610 & Vee = I R2 = 0.0169x7X103 Ves = 118-32 v 1 - --

(a) Charge on C, is given by, - Q, = C, v Now voltage across C, is equal to Ve, when S is closed. = Q, = C, Va, = 3x106x 67.61 - 10, = 2:03x104 cl closed. ) 3 X 10 - Ğ charge on C,

(b) Alor many milliseconds Clong time) 1 voltage across Cz is equal to applied voltage v which is equal to sum of VR, & Vaz = v= VR, + VR2 = 67.61 + 118:32 = 185.93.V So final charge on Cz is, Qef = C, V = 6*10^x 185.93 - Qu4 = 1.11558 x163 And Initial charge on Be Cz was, Q2i = CZ Ves = 6x106x118.32 Ozi = 0.70992 X10-3 C ... Change of charge on C₂ is, AQ = 0,4 - Qui = 1.11558x102-0.70992x163 100 = 0.406 x 103 cl