1. 5. Alternating Current Circuits
5.1 AC source characteristic
5.2 Resistor R in an AC circuit
5.3 Inductor L in an AC circuit
5.4 Capacitor C in an AC circuit
5.5 RLC series in an AC circuit.
5.6 Resonance in a series RLC circuit

2. How produce AC current

3. Some ways for AC generation

4. How translate AC current
Fig 33-CO These large transformers are used to increase the voltage at a power plant for distribution of energy by electrical transmission to the power grid. Voltages can be changed relatively easily because power is distributed by alternating current rather than direct current. (Lester Lefkowitz/Getty Images)

5. 5.1 AC Sources Characteristics
An AC circuit consists of electric elements ( Resistor, capacitor and inductor) and power source that provides an alternating voltage 
This time- varying voltage is described by
where ΔV max is the maximum output voltage of the ac generator
or the voltage amplitude
 Is the angular frequency which given by
Where  is the frequency of the generator (the voltage source) and T is the period.

6. The equation of Current  The phase angle ( )between V&I
We study the behavior of the electric elements R or L or C or RLC series in a AC circuit
Resistor R
Inductor L
Capacitor C
Want to known:
The equation of Current 
The phase angle ( )between V&I
The power energy P
Root mean square value (rms)
RLC series

7. 5.2 Resistor R in an AC Circuit
Consider a AC circuit consisting of a resistor R and AC source
By used Kirchhoff’s loop rule
the instantaneous current iR in the resistor is
the instantaneous current iR in is

8. Phase diagram of resistor R in AC circuit
We conclude that the current iR and the voltage R across the resistor R
The graph shows the variation current and the voltage across the resistor with time
The current  and the voltage  reach their maximum values at the same time. So we say the current and the voltage are in phase
i.e. = Current  and Voltage  in phase

9. Root mean square (rms) value of current (rms ) and voltage (Vrms)
Average power delivered to a resistor

10. From the equation we have Vmax = 200 V
Thus , the rms voltage
Therefore
and
max= rms x 2 = 1.41 x 2 = 2 A

11. 5.3 Inductors L in AC Circuit
Consider an AC circuit consisting an inductor connected to AC source
From EMF () across the inductor
 L= L=-L(di/dt) then apply Kirchhoff`s loop rule, we have
+  L = 0

12. We know cos t = - sin (t-/2)
The current of inductor is OR
where XL is the inductive reactanceالمعاوقة الحثية
Root mean square values

13. Phase diagram of L in an AC circuit
Active Figure 33.7 (a) Plots of the instantaneous current iL and instantaneous voltage vL across an inductor as functions of time. The current lags behind the voltage by 90°.
The current lags behind the voltage by 90°.
The current lags behind the voltage by 90°.
التيار يتاخر او يتخلف عن الجهد بزاوية مقدارها 90 درجة ( ¼ دورة)

14. EX: In a purely inductive ac circuit, L = 25 mH and the rms voltage is 150 V. Calculate the inductive reactance and rms current in the circuit if the frequency is 60 Hz.

15. Ex: An ac power supply produces a maximum voltage Vmax= 100 Volt
Ex: An ac power supply produces a maximum voltage Vmax= 100 Volt. This power supply is connected to a 24 resistor as figure. What is the rms current and rms voltage
EX: An inductor has a 54 reactance at 60 Hz. What is the maximum current when this inductor is connected to a 50 Hz source that produce a 100 V rms voltage

16. 5.4 Capacitor C in an AC Circuit
Consider an AC circuit consisting an capacitor connected to AC source
The current in a capacitor

17. Where the capacitive reactance XC is
The maximum current across the capacitor is OR
Where the capacitive reactance XC is
Root mean square values

18. التيار يتقدم على الجهد بزاوية مقدارها 90 ( ¼ دورة)
Phase diagram of C in an AC circuit
التيار يتقدم على الجهد بزاوية مقدارها 90 ( ¼ دورة)

20. 5.5. The RLC series in an AC circuit
Consider AC circuit consist of Resistor R , inductor L and capacitor C are connected in series
The instantaneous applied voltage is
And the instantaneous current is
Where is the phase angle between the current and the applied voltage

21.  is positive when XL >XC  is negative when XL < XC
The impedance Z of the circuit is
Phase angle 
 is positive when XL >XC
 is negative when XL < XC
 is zero when XL =XC

25. (E). Calculate the average power delivered to the RLC series circuit
From

28. 5.6 Resonance in series RLC Circuit
The resonance frequency ω 0 of a series RLC circuit occurs at XL-XC = 0 i.e (maximum current and Z=R ) . So
the angular resonance frequency 0 is
The resonance frequency f0 is