2-10-1

English

AC Circuit

This activity investigates the characteristics of a resistor, capacitor, coil (RCL) series circuit, which is connected to an AC power supply.

Theory

The electrical power sent from power generating stations to homes is alternating current (AC), not direct current (DC). Though direct current does not alternate with time, alternating current alternates according to a regular cycle, and this cyclical change can be expressed as a trigonometric function. When the voltage and frequency of a AC power supply are defined, the current flowing through the circuit has the same frequency as but a different phase from the power supply voltage. The phase difference and the magnitude of current depends on the component parts of the circuit. The voltage and current when a AC power supply is connected to a series circuit composed of a resistor, capacitor, and coil (RCL series circuit) can be expressed by the expressions shown below.

V = V0 cosω tI = I0 cos(ω t – φ) ω = 2πf

 

 

 

 

I0 =

 

 

V0

 

 

 

 

tanφ =

1

(Lω –

1

)

 

 

 

 

 

 

 

 

R

Cω

 

 

R2 + (Lω –

1

)2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cω

 

 

 

 

 

 

V (V)

: AC Power Supply Voltage

 

 

R(Ω)

: Resistance Value

 

V0 (V)

: Amplitude of AC Power Supply Voltage

 

C(F)

: Capacitor Capacitance

I (A)

: AC Current

 

 

 

 

L(H)

: Coil Self-inductance

I0 (A)

: Amplitude of AC Current

 

 

 

 

φ(rad)

: Current Phase Difference

ω (rad/s): Angular Frequency

 

 

 

 

t(s)

: Time

f (Hz)

: AC Frequency

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This activity investigates the voltage across the components of a series circuit. When a current that alternates with time is applied, the voltage across a capacitor and a coil is out of phase with the power supply voltage by -π/2 and π/2 respectively. The resistor does not have this characteristic, and so there is no phase lag. All of this means the peaks and valleys of the waveforms of the voltage across the components will be in different locations. The voltage across each of the components is expressed as follows.

VR = I0R VC =

I0

VL = I0 Lω VR (V) : Voltage Across the Resistor

Cω

 

 

VC (V) : Voltage Across the Capacitor

 

 

VL (V) : Voltage Across the Coil

We also know that the maximum current value is achieved using a capacitor-coil combination that satisfies the conditions shown below. A frequency like this is called a “resonant frequency.”

ω 2 = LC1

Activity:tivity: SetupSetup

￿Equipment

AC Power Supply (Switched)

Resistor

Capacitor

Coil

Voltage Measurement Setup (EA-200, graphic scientific calculator, data communication

cable, voltage probe (3))

￿Building the RCL Series Circuit

uBuild a circuit for a 3V, 50Hz power supply.

13V, 50Hz AC Power Supply

210Ω Resistor

3100∝ F Capacitor

410mH Coil

5Voltage Probe

6CH1

7CH2

8CH3

9EA-200

20020601