Question

A 212 Ω resistor, a 0.800 H inductor, and a 6.75 μFcapacitor are connected in series across a voltage source that has voltage amplitude 29.5 V and an angular frequency of 230 rad/s .

A) What is v at t= 22.0 ms ?

B) What is v_R at t= 22.0 ms ?

C) What is v_L at t= 22.0 ms ?

D) What is v_C at t= 22.0 ms ?

E) Compare v_C+v_L+v_R and v at this instant: v_C+v_L+v_R=v, v_C+v_L+v_R<v, or v_C+v_L+v_R>v

F) What is V_R?

G) What is V_C?

H) What is V_L?

I) Compare V and V_L+V_C+V_R:  V_L+V_C+V_R<V, V_L+V_C+V_R>V, or V_L+V_C+V_R=V

Answer 1

(a)

X_L = w*L = 230*0.8 = 184 ohm

Xc = 1/wC = 1/230*6.75*10^-6 = 644.12 ohm

Z = sqrt[ R² + (X_L - Xc)² ] = sqrt[(212)² + (460.12)²]

Z = 506.61 ohm

I = V/Z = 29.5/506.61

I = 0.0582 A

= tan^-1( (X_L - Xc)/R) = tan^-1(460.12/212)

= -1.13 rad

v = V*cos(w*t + ) = 29.5*cos(230*0.022 - 1.13)

v = -20.79 V

(b)

v_R = I*R*cosw*t = 0.0582*212*cos(230*0.022)

v_R = 4.20 V

(c)

v_L = I*X_L*cos(w*t + pi/2) = 0.0582*184*cos(230*0.022+pi/2)

v_L = 10.07 V

(d)

v_C = I*Xc*cos(w*t + -pi/2 ) = 0.0582*644.12*cos(230*0.022 -1.14 - pi/2)

v_C = -26.60 V

(e)

v_R + v_C + v_L = 4.20 - 26.60 + 10.07 = -12.33 V

and v = -20.79

v_R + v_C + v_L > v

(f)

V_R = I*R = 0.0582*212

V_R = 12.22V

(g)

V_L = I*X_L = 0.0582*184

V_L = 10.70 V

(h)

V_C = I*Xc = 0.0582*644.12

V_C = 37.48 V

(i)

V_R + V_L+ V_C = 12.22 + 10.70 + 37.48 = 60.4 V

V = 29.5 V

V_R + V_L+ V_C > V