The ratio of amplitude of V₂/V₁ for circuit shown below is :

Concept:

To find the ratio of amplitudes \( \frac{V_2}{V_1} \) in an AC circuit, use voltage division in the phasor domain considering the impedance of elements.

Given the source: \( 100 \cos(3t) \), the angular frequency is \( \omega = 3 \, \text{rad/s} \).

Given:

Resistors: 4Ω and 5Ω, Inductor: 1H, Capacitor: \( \frac{1}{36} \, F \)

Calculation:

Impedance of inductor: \( j\omega L = j3 \, \Omega \)

Impedance of capacitor: \( \frac{1}{j\omega C} = \frac{1}{j \cdot 3 \cdot \frac{1}{36}} = -j12 \, \Omega \)

The impedance of the right branch (Z_right):

\( Z = 5 - j12 \)

Magnitude of Z_right: \( |Z| = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \, \Omega \)

The impedance of the left branch (Z_left):

\( Z = 4 + j3 \Rightarrow |Z| = \sqrt{4^2 + 3^2} = \sqrt{25} = 5 \, \Omega \)

Total impedance: \( Z_{total} = Z_{left} + Z_{right} = 5 + 13 = 18 \, \Omega \)

Using voltage divider rule:

\( \frac{V_2}{V_1} = \frac{Z_{right}}{Z_{left}} = \frac{13}{5} = 2.6 \)

Correct Answer: 3) 2.6