Question

An RLC series circuit consists of a 450-?resistor, a 3.00-mF capacitor, and a 1.00-Hinductor. The circuit is driven by a power source that oscillates at 20.0 Hz and has an Erms value of 80.0V . The power source is switched on at t = 0 and at that instant the emf is at its maximum value.

What is the power supplied at t=.0200s, .0375s, and .0500s?

Answer 1

Power in R-L-C series circuit at any instant is given by:

P = E*I                                                ( E = alternating emf,   I = alternating current)

P = E₀ sinwt * I₀ sin ( wt - @)           ------------------------( 1 )    

    ( @ = phase difference between voltage and current, w = 2*pie*frequency)

E_rms = E₀ / 2^1/2

E0 ₌ E_rms * 2^1/2 = 80*1.414 = 113.13 Volt

I₀ = E₀ / Z                                            ( Z = total effective resistance = ( R² + ( X_L - X_c ) ² ) ^1/2

I₀ =   113.13/ 466.4                                    X_L = wL= 2*pie*f*L = 125.6 ohm,   X_c = 1/ wc = 1/ 2pie f*c = 2.65 ohm

I₀ = 0.2425 A                                                    Z = 466.4 ohm)

from impedence triangle , tan@ = X_L - X_c / R

@ = 15.28

(a) at t = .0200 s, by putting all the values in eq 1

Power = - 0.265 watt

( b) at t= .0375 , put all the values in eq 1

P = -0.407 watt

(c) at t= .0500 s

P = - 0.78 watt                ( from eq 1)

in above negative sign in power indicates this power if for negative cycle