Question

A series circuit has a resistor of 114 Ohms, an inductor of 79mH and a capacitor with value still to be decided. What values does the capacitor needs to have in order for the circuit to be in resonance?

Answer 1

To determine the value of the capacitor required for resonance in an RLC series circuit, one must set the inductive reactance equal to the capacitive reactance and use the resonant frequency formula to solve for the capacitance.

Step-by-step explanation:

To find the value of a capacitor that will make an RLC series circuit resonate, you need to set the inductive reactance equal to the capacitive reactance. The inductive reactance (№) is given by №L = 2πfL, and the capacitive reactance (№) is №C = 1 / (2πfC). At resonance, №L = №C, so we can solve for C to get C = 1 / (2πfL). To find the resonance frequency (f0) of the circuit, we use the resonance condition f0 = 1 / (2π√(LC)).

For the given values of a resistor of 114 Ohms, an inductor of 79mH, and an unknown capacitor value, we would first need to find the resonant frequency using the formula for an RLC circuit. Once we have f0, we could then find the necessary capacitance C that would make the circuit resonate using the resonant frequency equation.