A segment of a circuit is shown in the figure below. if VR=5V and Vc = 4 sin2t V, the voltage VL is
A segment of a circuit is shown in the figure below. if VR=5V and Vc = 4 sin2t V, the voltage VL is
Right Answer is:
32 sin 2t V
SOLUTION
Given
VR = 5V
Vc = 4 sin2t V
VL = ?
Applying KCL at the common node
IL = IC + 1 + 2
IL = IC + 3
Also
Ic = −Cdv/dt
$\begin{array}{l}{I_c} = -C\dfrac{{d{v_c}}}{{dt}}\\\\{I_c} = -1\dfrac{d}{{dt}}[4\sin 2t]\end{array}$
= −8 cos2t
IL = −8 cos2t + 3
Voltage across inductor
$\begin{array}{l}{V_L} = L\dfrac{{d{i_L}}}{{dt}}\\\\ = 2 \times \dfrac{d}{{dt}}[3 – 8\cos 2t]\end{array}$
VL = 32 sin2t V