An ac voltage of the form δv = 95 sin 275t where δv is in volts and t is in seconds, is applied to a series rlc circuit. if r = 38.0 ω, c = 26.0 µf, and l = 0.240 h, find the following. (a) impedance of the circuit
1 ω

(b) rms current in the circuit
2 a

(c) average power delivered to the circuit
3 w

(a) 83.06Ω

(b) 0.81A

(c) 25.0W

Explanation:

Comparing Δv = 95 sin 275t with Δv = Vmaxsinωt  

                        ω = 275

Inductive reactance Χ = ωL

                        = 275 × 0.240

                        = 66 Ω

Capacitive reactance Χ = 1/ωc

                        = 1/ (275 × 26 x 10^-6)

                        = 139.86Ω

Impedance Z =

                      =

                      =

                      = 83.06Ω  

(b)

solving for ,

substituting the value of and Z into equation, we have;

(c) Average power P = cos∅

To get the average power, we first solve for ∅ since it was not given.

                   ∅  

                   ∅  

                   ∅  

                   ∅  

                   ∅ = -62.77°  

Average power P = 0.81 × 67.2 × cos-62.77

                          P = 0.81 × 67.2 × 0.46  

                          P = 25.03872W              

                          P = 25.0W