Question

Please show all steps clearly, thank you.

The input to the series RLC bandpass filter designed in Problem 14.21 is 20 cos wt V. Find the voltage drop across the resistor when (a) w = woi (b) w = wel; (c) w = wc2; (d) w = 0.1w; (e) w = 10wo.
C = 5 nF, L = 79.16 mH, R = 1.99 kΩ, ωc1 = 39246.1 rad/s, ωc2 = 64378.8 rad/s

Answer 1

To find the voltage drop across the resistor in an RLC bandpass filter for different values of angular frequency (w), calculate the impedance of the circuit using the given values of capacitance, inductance, and resistance. Then, use Ohm's Law to calculate the current through the circuit. Finally, multiply the current by the resistance to find the voltage drop across the resistor.

Step-by-step explanation:

The voltage drop across the resistor in an RLC bandpass filter can be found by calculating the current through the circuit and then multiplying it by the resistance. The current can be calculated using Ohm's Law, where the voltage across the inductor (VL) and the voltage across the capacitor (VC) can be determined using the impedance of the circuit and the input voltage. The impedance is given by Z = √(R2 + (XL - XC)2), where XL is the inductive reactance and XC is the capacitive reactance.

For each scenario given:

1. Calculate the impedance of the circuit for the given ω using the formula above. Then calculate the current using Ohm's Law, I = V/Z. Finally, calculate the voltage drop across the resistor using Ohm's Law, VR = I * R.
2. Follow the same steps as in (a), but use the new value of ω.
3. Follow the same steps as in (a) and (b), but use the new value of ω.
4. Follow the same steps as in (a) and (b), but use the new value of ω.
5. Follow the same steps as in (a) and (b), but use the new value of ω.