If there is no resistance in either leg of a circuit with an inductance of 5 henrys in parallel with a capacitance of 1 microfarad, what is the equivalent impedance of the parallel network circuit?

If there is no resistance in either leg of a circuit with an inductance of 5 henrys in parallel with a capacitance of 1 microfarad, what is the equivalent impedance of the parallel network circuit?

• A. Zero
• B. Infinite
• C. Median
• D. None of the above

Answer: (B)

In a parallel LC circuit, the inductor and capacitor can be analyzed to find their combined effect on the current flowing through the circuit. The inductance of 5 henrys and capacitance of 1 microfarad will form a resonant circuit. When calculating the impedance in such a circuit, it's important to understand that the inductor's impedance (which increases with frequency) and the capacitor's impedance (which decreases with frequency) can lead to a situation where they effectively cancel each other out at resonance. In the absence of any resistance, this would result in the circuit offering no opposition to the flow of current, theoretically leading to infinite current. Since impedance is defined as the total opposition to current in an AC circuit, when the frequency of the source matches the resonant frequency of the tank circuit formed by the inductor and capacitor, the impedance approaches zero. However, without real-world resistive elements, we can state that the impedance approaches an ideal condition of being infinite which corresponds with a perfect LC circuit in parallel at resonance. Therefore, the condition described in the question aligns with the fact that the impedance of the entire parallel network without any resistance present is considered infinite. This reflects that the circuit does not dissipate any power,

In a parallel LC circuit, the inductor and capacitor can be analyzed to find their combined effect on the current flowing through the circuit. The inductance of 5 henrys and capacitance of 1 microfarad will form a resonant circuit.

When calculating the impedance in such a circuit, it's important to understand that the inductor's impedance (which increases with frequency) and the capacitor's impedance (which decreases with frequency) can lead to a situation where they effectively cancel each other out at resonance. In the absence of any resistance, this would result in the circuit offering no opposition to the flow of current, theoretically leading to infinite current.

Since impedance is defined as the total opposition to current in an AC circuit, when the frequency of the source matches the resonant frequency of the tank circuit formed by the inductor and capacitor, the impedance approaches zero. However, without real-world resistive elements, we can state that the impedance approaches an ideal condition of being infinite which corresponds with a perfect LC circuit in parallel at resonance.

Therefore, the condition described in the question aligns with the fact that the impedance of the entire parallel network without any resistance present is considered infinite. This reflects that the circuit does not dissipate any power,