Chapter 1

Q. 1.P.16

Q. 1.P.16

A segment of a circuit is shown in the following figure. At V_{ R }=5 V , V_{ C }=4 \sin 2 t . \text { Find } V_{ L }  .

(a) 16 sin2t V      (b) 32 sin2t V

(c) 16 cos2t V       (d) 32 cos2t V

1.1.16

Step-by-Step

Verified Solution

Applying KCL, we get

\begin{array}{r} -2 A -i_{ R }+i_{ L }+i_{ C }=0 \\ -2-\frac{5}{5}+i_{ L }+1 \times \frac{d}{d t}(4 \sin 2 t)=0 \\ -2-1+i_{ L }+4 \cos 2 t(2)=0 \\ i_{ L }=3-8 \cos 2 t \end{array}

Now, V_{ L }=L \cdot \frac{d i_{ L }}{d t}=2 \times(0-8(-\sin 2 t) \times 2)=32 \sin 2 t

V_{ L }=32 \sin 2 t  V