Question

Physics 113 Worksheet 2 Spring 2019 Problem2 470 nF 33nFJ 2.2 uF 4.7 uF 3.3 uF Figure 1: Capacitor Network Define Δ V-Va-H4-10V and calculate the following: (3 Points) Calculate the Equivalent Capacitance, G. of the circuit shown in Figure 1. (3 Points) Calculate the Charge on the Equivalent Capacitance, (3 Points) Calculate the Voltage at PointJ in Figure 1 with respect to Terminal B. Problem 3 Assume B-(x +y)R+(-2x+3y) . (3 Points) Calculate the Scalar Product, A B . (3 Points) Calculate the Vector Product, A xB

Answer 1

1/C_11 = 1/470 nF + 1/2.2 muF C_11 = 2.2 times 0.47/2.2 + 0.47 muF = 0.387 muF C_s = 4.7 + 3.3 muF = 8 muF C_eq = 8 times 0.42/(8 + 0.42) muF = 0.399 muF Charge = C_eq times V = 0.399 times 10 mu C = 3.99 mu C \r\n charge in 0.42 muF = 3.99 muC charge across 0.387 muF = Q Q/0.387 = 3.99/0.42 muC Charge across (Q) = 3.6765 muC voltage across 470 nF = 3.6765/0.47 = 7.82V Voltage at J w.r.t B = 10 - 7.82 V = 2.18V \r\n A vector = (3x - 2y)x^^+ (x - y) y^^B vector = (x + y)x^^+ (-2x + 3y)y^^A vector middot B vector = (3x - 2y)(x + y) + (x - y)(-2x + 3y) = 3x^2 - 2yx + 3xy - 2y^+ (-2)x^2 + 3xy + 2xy - 3y^2 = x^2 (1) + xy(-2 + 3 + 3 + 2) + y^2 (-2 - 3) = x^2 + 6xy - 5y^2 A vector times B vector = Vertical-bar x^^(3x - 2y) (x + y) y^^(x - y) (-2x + 3y) z^^0 0 Vertical-bar