1.

Introduction
Alternating current (AC) circuits are circuits where the current
changes direction periodically. Unlike direct current (DC)
circuits, where the current flows in one direction, AC circuits
use sinusoidal signals, which vary in both amplitude and
direction. Capacitors and inductors are two important
components in AC circuits, each influencing the circuit’s
behavior in unique ways.
Capacitors and Inductors in AC Circuits
 Capacitors store energy in the form of an electric field
between two conductors.
 Inductors store energy in the form of a magnetic field
generated by a current passing through a coil of wire.
In AC circuits, both capacitors and inductors create
impedance, which resists the flow of current. However, unlike
resistors, they don’t dissipate energy but rather store it
temporarily. Capacitors and inductors cause phase shifts
between the voltage and current, a crucial aspect of their
operation in AC circuits.
2. capacitors in AC circuit
6Power in AC Circuits
Power in AC circuits is defined as the rate at which electrical
energy is converted into another form, such as heat, light, or
mechanical energy. AC power is typically classified into three
types: real power (P), reactive power (Q), and apparent
power (S). Real power (measured in watts, W) represents the
actual energy consumed by the resistive components of the
circuit, such as lights and heating elements. Reactive power
(measured in volt-amperes reactive, VAR) is associated with
inductive and capacitive components and does not
contribute to energy consumption but is necessary for
maintaining magnetic and electric fields. Apparent power
(measured in volt-amperes, VA) is the total power supplied
by the source. The relationship between real and apparent
power is described by the power factor, which is the cosine
of the phase angle between the voltage and current
waveforms. A higher power factor means more efficient
energy usage. Power factor correction, often achieved with
capacitors, is crucial in industrial applications to improve
efficiency and reduce energy losses.
8. Real-World Applications of Capacitors and Inductors
Capacitors and inductors are essential components used
across a wide range of real-world applications in both
industrial and consumer electronics. Capacitors are primarily
used for energy storage, signal filtering, and smoothing
power supplies in devices such as televisions, radios, and
power systems. They are also crucial in power factor
correction, which helps improve the efficiency of electrical
systems by compensating for inductive loads. In signal
processing, capacitors help filter out unwanted frequencies.
Inductors, on the other hand, are key components in
transformers, motors, and inductive heating systems. They
are also used in radio frequency circuits for tuning
applications, such as in radios or TVs, where they help select
a specific frequency from a range of signals. Additionally,
inductors are used in filters to block or pass certain
frequencies. Both capacitors and inductors are integral to
power distribution systems, wireless communication, and
many other technologies that rely on AC circuits for proper
operation.

9.
Experiment: Investigating the Effect of Capacitors and Inductors on Phase
Difference and Impedance in an AC Circuit

Objective
To study the effect of capacitors and inductors on the phase difference between voltage and
current, and to understand their impedance in an AC circuit.

Apparatus

 AC power supply (variable frequency)

 Capacitor (100 µF)
 Inductor (100 mH)
 Resistor (100 Ω)
 Connecting wires
 Multimeter
 Oscilloscope
 Function generator (if available)
 Rheostat (optional, for controlling current)

Theory

In an AC circuit, capacitors and inductors affect the phase relationship between the applied
voltage and the resulting current. A capacitor causes the current to lead the voltage by 90°,
while an inductor causes the voltage to lead the current by 90°. The total opposition to current
flow in an AC circuit is called impedance (Z). The impedance of a capacitor is
XC=1ωCX_C = \frac{1}{\omega C}XC=ωC1, and the impedance of an inductor is
XL=ωLX_L = \omega LXL=ωL, where ω=2πf\omega = 2\pi fω=2πf is the angular frequency
of the AC supply. The objective is to observe how these components change the phase
difference and impedance.

Procedure

1. Setup Circuit for Resistor-Only AC Circuit:

o Connect the AC power supply to a simple circuit consisting of the resistor
(100 Ω) and the multimeter (for measuring current).
o Turn on the AC supply at a specific frequency (e.g., 50 Hz) and set the voltage
to a known value (e.g., 10V).
o Use the oscilloscope to measure the waveform of the applied voltage and the
current through the resistor.
o Record the phase difference between the voltage and current. In a purely
resistive circuit, they should be in phase (0°).
2. Replace Resistor with Capacitor:
o Disconnect the resistor and replace it with the capacitor (100 µF).
o Observe the voltage and current waveforms on the oscilloscope.
o Measure and record the phase difference between the voltage and current. In a
capacitive circuit, the current should lead the voltage by 90°.
o Note the impedance of the capacitor at this frequency. The impedance can be
calculated using XC=1ωCX_C = \frac{1}{\omega C}XC=ωC1.
3. Replace Capacitor with Inductor:
o Now, replace the capacitor with the inductor (100 mH).
o Measure the voltage and current waveforms again.
o Record the phase difference between the voltage and current. In an inductive
circuit, the voltage should lead the current by 90°.
 o Calculate the impedance of the inductor at this frequency. The impedance of
the inductor is XL=ωLX_L = \omega LXL=ωL.
4. Varying Frequency (Optional):
o Change the frequency of the AC supply and repeat the measurements for the
capacitor and inductor.
o Observe how the impedance and phase differences change with frequency. At
higher frequencies, the capacitive reactance decreases, and the inductive
reactance increases.

Observations

 Resistor-only Circuit: Voltage and current are in phase (0° phase shift).
 Capacitor-only Circuit: The current leads the voltage by 90° (a quarter cycle).
 Inductor-only Circuit: The voltage leads the current by 90° (a quarter cycle).

Record the impedance of each component at the given frequency.

Calculations

1. For the capacitor:

XC=1ωCX_C = \frac{1}{\omega C}XC=ωC1

where ω=2πf\omega = 2 \pi fω=2πf and C=100 μFC = 100 \, \mu FC=100μF.

2. For the inductor:

XL=ωLX_L = \omega LXL=ωL

where L=100 mHL = 100 \, mHL=100mH and fff is the frequency.

Precautions

 Ensure that the circuit connections are properly insulated to avoid short circuits or
accidental shocks.
 Always start with a low frequency when testing the circuit to avoid damaging the
components.
 Make sure to connect the oscilloscope probes correctly to measure voltage and current
waveforms.

Result and Discussion

 In the resistor-only circuit, there is no phase shift between the voltage and current,
confirming that resistors do not cause phase differences in AC circuits.
 In the capacitor-only circuit, the current leads the voltage by 90°, showing that
capacitive reactance causes this phase shift.
 In the inductor-only circuit, the voltage leads the current by 90°, which is a
characteristic behavior of inductive reactance.
 The impedance of the capacitor decreases as the frequency increases, and the
impedance of the inductor increases with frequency.
Conclusion

This experiment demonstrates how capacitors and inductors influence the phase relationship
and impedance in AC circuits. Capacitors cause the current to lead the voltage, while
inductors cause the voltage to lead the current. The experiment also highlights the frequency
dependence of impedance in capacitors and inductors.

10. Conclusion

Capacitors and inductors play essential roles in determining the behavior of AC circuits.
Capacitors introduce a phase shift where current leads voltage, and their impedance decreases
with increasing frequency. Inductors, on the other hand, cause voltage to lead the current, and
their impedance increases with frequency. The combination of these components in series or
parallel configurations leads to the formation of complex circuits with resonance phenomena,
affecting current, voltage, and impedance. These circuits are used in a wide range of
applications, such as power factor correction, filtering, resonance tuning, and energy storage.
The ability to control the flow of current and voltage through capacitors and inductors allows
engineers to design efficient electrical systems. Understanding the properties of capacitors
and inductors in AC circuits is fundamental for designing and optimizing circuits in
telecommunications, power systems, consumer electronics, and industrial applications. The
experiment conducted shows the significance of phase shifts and reactance in shaping circuit
behavior, providing hands-on insights into their functionality.