2. Alternating Current (AC)
• Alternating current (AC): current that changes its magnitude
and direction periodically.
3. Alternating Current (AC)-Current (I)at time (t)
The current at time (t) in AC circuit can be found by the equation:
𝐼 = 𝐼𝑚𝑎𝑥 sin 2𝜋𝑓𝑡 = 𝐼𝑚𝑎𝑥 sin
(𝜔𝑡)1
I: Current at time t (Ampere)
Imax: Maximum value of current (Ampere)
f: Frequency (number of cycles per second) (Hertz)
t: Time (Second)
ω: Angular frequency (rad/second)
1: use radian mode in calculations
4. Alternating Current (AC)-Potential Difference (ΔV) at time(t)
∆𝑉 = ∆𝑉
𝑚𝑎𝑥 sin 2𝜋𝑓𝑡 + 𝜑 = ∆𝑉
𝑚𝑎𝑥 sin
(𝜔𝑡 + 𝜑)1
ΔV: Potential difference at time t (Volt)
Imax: maximum value of potential difference (Volt)
f: Frequency (number of cycles per second) (Hertz)
t: Time (Second)
ω: Angular frequency (rad/second)
φ: Phase difference (radian)2
1: use radian mode in calculations
2:Phase difference will be explained in more details in LCR circuit
6. Alternating Current (AC)-Ohms Law
When an AC source is connected to passive components, ohm’s law can apply as:
∆𝑉 = 𝐼𝑧 , ∆𝑉
𝑚𝑎𝑥 = 𝐼𝑚𝑎𝑥 𝑧
z: Impedance (Ohm)
Impedance is the total current hindrance offered by the passive components in the circuit.
7.
8. LCR Circuit
• LCR circuit: a circuit in which a resistor , capacitor and an inductor
are connected in series with an AC power supply.
• The current in the circuit is the same at any point.
• The total potential difference in LCR circuit is:
∆𝑉 = ∆𝑉
𝑚𝑎𝑥sin 𝜔𝑡 + 𝜑
unit of ϕ is radian
𝐼 = 𝐼𝑚𝑎𝑥 sin
(𝜔𝑡)
9. LCR Circuit
• The impedance of the LCR circuit is:
𝑧 = 𝑅2 + 𝑋𝐿 − 𝑋𝐶
2
• The phase difference between current and voltage in LCR
circuit can also be found by:
• 𝑡𝑎𝑛𝜑 =
𝑋𝐿−𝑋𝐶
𝑅
16. LCR Circuit
-Resonance frequency
• if the frequency of an AC source of an LCR circuit
was increased the current increases till it reaches a
maximum value. Then if the frequency was
increase more, the current starts to drop.
• At that particular frequency where the current
peaks, the circuit is said to operate at resonance
frequency (fr).
• Note the following point when a circuit is operating
at resonance frequency is:
XL =XC.
z=R, which is minimum value of impedance.
current is at maximum value.
18. LCR Circuit
-Resonance frequency
• The resonance frequency of a particular LCR circuit depends
only on the inductance (L) and capacitance (C) in the circuit.
𝑓𝑟 =
1
2𝜋 𝐿𝐶
fr: Resonance frequency (Hertz)
L: Inductance (Henry)
C: Capacitance (farad)
