# 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

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