TeXes Science Practice Test

What is the rms potential drop across the resistor at resonance in the described RLC circuit?

1. 100 V

2. 150 V

3. 200 V

4. 250 V

The correct answer is: 200 V

In an RLC circuit at resonance, the behavior of the circuit components interacts in a specific way that maximizes the current through the circuit. At resonance, the inductive reactance and capacitive reactance are equal in magnitude but opposite in phase, effectively canceling each other out. This results in the circuit being purely resistive, and the total impedance is minimized to just the resistance value. The rms potential drop across the resistor can be calculated by considering the maximum current that flows through the circuit at this frequency. Since the resonant frequency allows for maximum current due to the decreased impedance, the potential drop across the resistor is determined using Ohm’s law: V = I*r, where V is the potential drop, I is the rms current, and r is the resistance. In this case, the potential drop across the resistor at resonance is stated to be 200 V, which indicates the circuit's characteristics and the specific values of voltage, current, and resistance align with the principles of resonance in an RLC circuit. This value reflects the inherent properties of the circuit under these resonant conditions. To summarize, the potential drop of 200 V at resonance signifies the optimal performance of the circuit, demonstrating the relationship between voltage, current, and