Casio EA-200, EA200 VC = V – VR = V (1– e, VC = VR = Ve–, VL = VR – V = – Ve L, VL = VR = Ve–, Equipment, ￿Equipment, ￿Building the RC Series Circuit

Direct Current and Transient Phenomena

This activity investigates transient phenomena when direct current flows through a capacitor and coil.

Theory

Generally speaking, electrical current is the movement of free electrons within metal. When electrical current flows through a capacitor, electrons are accumulated, and the capacitor stores the charge. The accumulation of an electrical charge is called “charging,” while the loss of the charge by the capacitor is called “discharging.”

Connecting a resistor and capacitor serial circuit to a D.C. power supply causes current to flow to the capacitor, which charges until it reaches a steady state. Now if the power supply is removed and the circuit is closed, current flows to the capacitor again, which now discharges until it reaches a steady state. Current flows to the capacitor in the opposite direction that it flowed during charging. The change in capacitor voltage during the transient phase until the capacitor reaches a steady state, while charging and discharging is represented by the expression shown below.

		–	t
VC = V – VR = V (1– e			RC	)	1 Charge Circuit
VC = VR = Ve–	t				2 Discharge Circuit
	RC

VR (V): Voltage Across the Resistor

VC (V): Voltage Across the Capacitor

V (V) : Power Supply Voltage

R (Ω) : Resistance

C (F) : Capacitance

t (s) : Time

When the current flowing through a coil changes over time, the coil induces voltage, like an electrical generator. This is called “self-induced electromotive force,” which acts to oppose the change in current. When a D.C. power supply is connected in a resistor and coil series circuit, the effect of the coil’s self-induced electromotive force can be observed until current reaches a fixed value. Similarly, self-induced electromotive force can also be observed by cutting off the power supply to a circuit through which steady current is flowing.

The change in coil voltage during these transient phases is represented by the expressions below.

– R t

VL = VR – V = – Ve L

VL = VR = Ve–	R	t	1 Circuit With
	L
VR (V): Voltage Across the Resistor			Power Supply
			2 Circuit Without
VL (V): Voltage Across the Coil			Power Supply
V (V) : Power Supply Voltage
R (Ω) : Resistance
L (H) : Self-inductance
t (s) : Time

2-9-1

English

Activity:tivity: SetupSetup

￿Equipment

Battery (D.C. Power Supply) Resistor Capacitor Coil Switch

Voltage Measurement Setup (EA-200, graphic scientific calculator, data communication cable, voltage probe)

￿Building the RC Series Circuit

uThe product of the resistance value and the capacitor’s capacitance should be around 1.

1 3V D.C. Power Supply

2Switch

310kΩ Resistor

4100∝ F Capacitor

5Voltage Probe (CH1)

6EA-200

￿Building the RL Series Circuit

uThe quotient when the resistance value is divided by the self-inductance of the coil should be around 1.

13V D.C. Power Supply

2Switch

30.1Ω Resistor

4100mH Coil

5Voltage Probe (CH1)

6EA-200

20020601