This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Calculate the capacitive reactance. The source frequency is f = 10\,Hz and the capacitance is C = 4.7\, F. First, calculate the angular frequency : = 2 f = 2 (10\,Hz) = 20\,rad/s Next, calculate the capacitive reactance X_C: X_C = (1)/( C) = (1)/(20 × 4.7 × 10^-6)\,F X_C = (1)/(295.3097 × 10^-6)\, ≈ 3386.3\, The impedance of the capacitor is Z_C = -jX_C = -j3386.3\,. Step 2: Determine the output voltage for (a) R1 open. If R_1 is open, it creates an open circuit in series with the voltage source. No current can flow through the circuit. Since no current flows through R_2 or C, there will be no voltage drop across them. Therefore, the output voltage V_out is 0 V. Step 3: Determine the output voltage for (b) R2 open. If R_2 is open, the resistor R_2 is removed from the circuit. The circuit becomes a series combination of R_1 and C. The total impedance of this series circuit is Z_total = R_1 + Z_C = 10\,k - j3386.3\,. The output voltage V_out is measured across the capacitor C. Using the voltage divider rule: V_out = V_s (Z_C)/(R_1 + Z_C) V_out = 1\,V (-j3386.3\,)/(10000\, - j3386.3\,) The magnitude of the output voltage is: |V_out| = 1\,V (|-j3386.3\,|)/(|10000\, - j3386.3\,|) |V_out| = (3386.3)/(sqrt((10000)^2 + (-3386.3)^2)) |V_out| = (3386.3)/(sqrt(100 × 10^6 + 11.467 × 10^6)) = 3386.3111.467 ×