Question

Question 6. We think of the response of the circuit as the ratio of the maximum current to the maximum voltage provided. Explain why the ratio of the maximum current to the maximum current of the entire circuit will be largest when the two reactances are equal. When this is the case, we think of the RLC circuit as responding as strongly as possible to the AC current and say that it is resonating.

Answer 1

Impedance (Z) of any AC circuit is given by the formula,

Z = √{R2^{​​​​​2} + (X_{​​​​​​L} - X_{​​​​​​C})²} where,

R is the resistance in the circuit,

X_{​​​​​​L} is the inductive reactance, (=L) where is the angular frequency and L is the inductance of the inductor.

And X_{​​​​​​C} is the capacitive reactance, (1/C) where is angular frequency and C is the capacitance of capacitor.

Here, Z = V_{​​​​​​max}/I_{​​​​​​max} ,

I_{​​​​​​max} = V_​​max/Z ,

Since maximum current is inversely proportional to Z, therefore the maximum current in the circuit will be maximum for minimum value of Z.

Since both the reactance depends upon the angular frequency of the AC source, and resistor is a constant resistance.

So, on changing angular frequency, reactances change, and at some point of time the angular frequency may be set as in order to cancel the reactances.

And thus giving the minimum value of Z (=R). And the maximum current is maximized.