Word Count : 695

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Let's solve each part numerically, step by step, manually. --- ## (a) Wien Bridge Oscillator ### Working Principle: A Wien bridge oscillator is a sinusoidal oscillator that uses a bridge circuit (series and parallel RC combination) to provide positive feedback at a particular frequency. * It consists of: * Frequency-determining network: Two resistors $R_1, R_2$ and two capacitors $C_1, C_2$ in a series-parallel combination. * Amplifier: Usually an op-amp, providing gain to sustain oscillations. * Frequency of oscillation: $$ f = \frac{1}{2\pi RC} \quad \text{(if } R_1 = R_2 = R, \; C_1 = C_2 = C\text{)} $$ * Gain condition: To sustain oscillation, the amplifier gain $A$ should satisfy: $$ A = 3 \quad \text{(for standard op-amp Wien bridge)} $$ --- ### Numerical Calculation: Given: $$ f = 5\,\text{kHz}, \quad C = 1\,\text{nF (assuming "pF" given means 1 nF)} $$ We can calculate R: $$ R = \frac{1}{2\pi f C} $$ Step by step: $$ R = \frac{1}{2 \pi \cdot 5000 \cdot 1 \times 10^{-9}} $$ 1. Compute $2 \pi f C$: _______ ____ ____ _______ ___ ___ _______ __________ __________.
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