- #1

- 2,076

- 140

## Homework Statement

Find ##i(t)## in the following circuit:

## Homework Equations

##Z = \frac{V}{I} \Rightarrow I = \frac{V}{Z}##

## The Attempt at a Solution

I've solved this, but I'm wondering why my answer is different than the book's answer. The book lists the answer as ##i(t) = 3.88 cos(377t - 39.2^o) \space A##.

Writing the given voltage as a phasor: ##v(t) = 120 \angle 60^o \space V##.

Calculating the impedances of each component:

##Z_R = 20 \Omega##

##Z_L = j \omega L = (377)(40 \times 10^{-3})j = (15.08j) \Omega##

##Z_C = - \frac{j}{\omega C} = - \frac{j}{(377)(50 \times 10^{-6})} = -(53.05j) \Omega##

Calculating the required equivalent impedances:

##Z_{eq_1} = Z_R + Z_L = (20 + 15.08j) \Omega##

##Z_{eq_2} = (\frac{1}{Z_C} + \frac{1}{Z_{eq_1}})^{-1} = (- \frac{1}{53.05 j} + \frac{1}{20 + 15.08j})^{-1} = (30.56 + 4.97j) = 30.96 \angle 9.24^o \space \Omega##

Finding the current phasor:

##I = \frac{V}{Z} = \frac{120 \angle 60^o}{30.96 \angle 9.24^o} = 3.88 \angle 50.8^o \space A##

##i(t) = 3.88 cos(377t + 50.8^o) \space A##

My answer differs from the books answer by exactly ##90^o## (50.8 + 39.2 = 90). Why is this? Have I done something wrong?