A segment of a circuit is shown in the figure given below. v_{ R }=5 V , v_{ C }=4 \sin 2 t . \text { The voltage } v_{ L } is given by

(a) 3 – 8cos2t (b) 32sin2t

(c) 16sin2t (d) 16cos2t

Step-by-Step

Learn more on how do we answer questions.

Applying Kirchhoff’s current law, sum of incoming currents is equal to sum of outgoing currents.

i_{ L }=i_{ C }+1+2 \Rightarrow i_{ L }=i_{ C }+3

We know that

i_{ C }=-C \frac{d v_{ C }}{d t}=-1 \cdot \frac{d}{d t}(4 \sin 2 t)=-8 \cos 2 t

Therefore, i_{ L }=-8 \cos 2 t+3

\begin{aligned} v_{ L } & =L \frac{d i_{ L }}{d t}=2 \times \frac{d}{d t}(-8 \cos 2 t+3) \\ & =2[8 \cdot \sin 2 t \cdot 2+0]=32 \sin 2 t \end{aligned}

Question: 1.SGPYQ.27

i_{ L }\left(0^{-}\right)=\frac{\text { To...

Question: 1.SGPYQ.28

E_1 is the stored energy and [lat...

Question: 1.SGPYQ.26

To find the Thevenin voltage open circuit the term...

Question: 1.SGPYQ.1

Power is the rate of change of energy.
Therefore,
...

Question: 1.SGPYQ.3

Given that
Z_1=10 \angle-60^{\circ}, Z_2=1...

Question: 1.SGPYQ.4

Given that for resonance
\left|V_{ L }\rig...

Question: 1.SGPYQ.5

At node P,
\begin{aligned} & 2+\frac{V...

Question: 1.SGPYQ.6

For maximum power transfer,
R_{ L }=\left|...

Question: 1.SGPYQ.7

The equivalent circuit is
Applying nodal analysis ...

Question: 1.SGPYQ.8

At t < 0; V_C\left(0^{-}\right)=0 ; \qu...