Question

The electrical circuit shown below contains five resistors in paraliel and a vollage source R2 To calculate the effective resistance of a circuit with resistors in parallel, the following equation can be used: ReffectiveR, R2 R .a. If the resistance of each resistor is labelled R, to R, Write the effective resistance of the circuit in sigma notation. b. The voltage applied to the circuit varies with time, t, and the initial voltage variation applied to the circuit is described by the function Find a binomial series approximation of the voltage using the first three terms of the series. f(t)- (1 +t)i ii. Find the voltage approximation at time t = 0.8 seconds, giving your answer to two significant figures

Answer 1

a) Effective resistance in sigma notation 1/R_effective = sigma^5_i = 1 1/R_i b) i) Binomial series is given by (If x)^n = I + nx + n(n minus 1)/2! X^2 + n(n minus 1) (n minus 2)3! X^3 + ---- given f(t) = (1 + t)^3/2 for final three term. f(t) = T + 3/2 t + 3/2 times (3/2 minus 1)/2! t^2 V = f(t) = 1 + 3/2 t + 3/8 t^2 ii) at t - 0.8 sec f(0.8) = I + 3/2 t + 3/8 t^2 = I + 3/2 (0.8) + 3/8 (0.8)^2 v = 61/25 = 2.44 V