Final answer:
The voltage drop across a resistor in an RLC bandpass filter when driven at its resonant frequency and at frequencies away from resonance can be calculated using Ohm's Law, depending on the resistance and other circuit parameters.
Step-by-step explanation:
To find the voltage drop across the resistor in an RLC bandpass filter, we need to know the resistance value and the specific circuit parameters, which are not provided in the question. However, we can discuss the general process. The voltage drop across a resistor in an RLC circuit when an input of 20cosωt V is applied can be found using Ohm's Law, which is V = IR, where I is the current through the resistor and R is the resistance. At the resonant frequency (ω=ω₀), the impedance of the circuit is at its minimum and equals the resistance of the resistor due to the inductive and capacitive reactances canceling each other out. The current I and voltage V across the resistor will be at maximum in this case. For frequencies away from resonance (ω=ω₁ and ω=ω₂), the impedance will be higher, and the voltage drop across the resistor will be lower. For ω=0.1ω₀ and ω=10ω₀, the circuit behaves mainly as a capacitive or inductive reactance respectively, and the voltage drop across the resistor will significantly differ from the resonant case. The exact values would require calculation based on the circuit parameters.