Answer to Question #278276 in Differential Equations for Jericho

Question

A circuit has in series an electromotive force given by E=40-sin35tV, a resistor of 10Ω, and an inductor of 0.4H . If the initial current is 2 , find the current at time t>2.

Answer 1

$X_L = wL =35\cdot0.4= 14\ Ω$

$Z = R + jwL = 10 + j14\ Ω$

The magnitude of Z:

$Z = \sqrt{R^2 + (wL)^2} = \sqrt{10^2 +14^2} = 17.20\ Ω$

The phase angle of Z:

$\varphi = tan^{-1} ( wL/R) = tan^{-1} (14/10) = 54°=0.94$ rad

current:

$I(t)=2sin(35t-0.94)$

$I(2)=2sin(70-0.94)=-0.11$ A