Now, let\'s combine the ideas above and consider an AC circuit containing all of

Question

Now, let's combine the ideas above and consider an AC circuit containing all of the components discussed so far, connected in series with the alternating voltage source. For short, we call this an RCL circuit. The total impedance and the current for this RCL circuit are given by: Z = squareroot R^2 + (X_L - X_C)^2 and I = V/Z = V/squareroot R^2 + (X_L - X_C)^2 Using these equations, answer the following questions: In the equation for the total impedance, Z, you see a (X_L - X_c) term. Why do you think we must subtract these two impedances in order to help find the total impedance? Based on your answer above, why is R left alone in the equation for Z ? What would happen to the total impedance Z if the inductive reactance X_L and capacitive reactance X_c are equal? At what frequency f does this happen? This value of f is known as the resonance frequency, f_o. At this frequency, an RCL circuit's current is at a maximum. This will be an importance concept to keep in mind!

Explanation / Answer

a)The phase of voltage across inductor and capacitor are out of phase.

b) The voltage across R is always in phase with source.

c) when, XL = XC

z = sqrt(R^2 + (XL_XC)^2)

= R

let f is the frequency.

XL = XC

2*pi*f*L = 1/(2*pi*f*C)

f^2 = 1/(4*pi^2*L*C)

f = 1/(2*pi*sqrt(L*C)

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