A circuit has a resistor with a resistance of3Ωfollowed by three parallel branches, each holding a resistor with a resistance of5Ω. What is the total equivalent resistance of the circuit?a)15/3Ωb)14/3Ωc)15/7Ωd)19/3ΩCorrect answer is option 'B'. Can you explain this answer?

Question

A circuit has a resistor with a resistance of3&Omega;followed by three parallel branches, each holding a resistor with a resistance of5&Omega;. What is the total equivalent resistance of the circuit?a)15/3&Omega;b)14/3&Omega;c)15/7&Omega;d)19/3&Omega;Correct answer is option 'B'. Can you explain this answer?

Answer

Ohms, a capacitor with a capacitance of 2 microfarads, and an inductor with an inductance of 5 millihenries.

This circuit is a series circuit, meaning that the components are connected one after the other in a single path. The current flows through each component in the same direction.

The behavior of this circuit depends on the frequency of the applied voltage. At low frequencies, the capacitor acts as an open circuit, and the inductor acts as a short circuit. Therefore, the resistance of the resistor dominates the behavior of the circuit, and the current flows mostly through the resistor.

At high frequencies, the capacitor acts as a short circuit, and the inductor acts as an open circuit. Therefore, the resistance of the resistor becomes less important, and the current flows mostly through the capacitor and the inductor.

At a certain frequency, called the resonant frequency, the capacitive reactance and the inductive reactance cancel each other out, and the impedance of the circuit becomes purely resistive. At this frequency, the current is maximized, and the circuit is said to be resonant.

The resonant frequency can be calculated using the formula:

f = 1 / (2π√(LC))

where f is the resonant frequency in Hertz, L is the inductance in Henrys, and C is the capacitance in Farads.

For this circuit, the resonant frequency is:

f = 1 / (2π√(5mH x 2μF)) = 159.2 Hz

At this frequency, the circuit will exhibit maximum current flow.

Answer

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