AC vs DC and Circuit Analysis Notes q

Definitions

  • Direct Current (DC): Flow of electric current in one direction, with a constant voltage source, often used in batteries and electronic devices. DC is characterized by constant voltage levels and is commonly utilized in applications requiring stable power supplies, like electronic circuits, flashlights, and various devices that depend on batteries.

  • Alternating Current (AC): Electric current that periodically reverses direction, commonly used in power supply systems due to its efficiency in long-distance transmission. AC is essential for powering homes and businesses, and it can be generated from various sources including hydroelectric plants, fossil fuels, and wind energy. The ability to transform AC voltage levels is a major advantage, facilitating its distribution.

Characteristics of AC and DC

  • Alternating Current (AC):

    • Direction of current reverses at regular time intervals, typically in a sinusoidal pattern, making AC preferable for most electrical needs.

    • Graph of AC shows alternating maxima—positive maxima (right) and negative maxima (left) over time, reflecting the periodic nature of AC.

    • Benefits include reduced line losses over long distances and ease of transformation to different voltages, making it adaptable for diverse applications from residential to industrial.

  • Direct Current (DC):

    • Voltage and current are constant over time once established, represented as straight lines in graphs, making it easier to predict power usage.

    • Commonly used in low-voltage applications and electronic circuits, with limited distance transmission due to voltage drop over lines. Typical applications include rechargeable batteries, photovoltaic systems, and low-voltage power supplies.

Voltage and Current in AC

  • AC voltage can be expressed mathematically:

    • V(t) = V_0 \times \text{sin}(2 \text{π} f t)

    • Where:

    • V: Voltage at time t

    • V_0: Peak voltage

    • f: Frequency (Hz)

  • Current for AC also follows a sinusoidal pattern:

    • I(t) = I_0 \times \text{sin}(2 \text{π} f t)

    • Where:

    • I: Current at time t

    • I_0: Peak current

  • Power in AC:

    • Average power can be calculated when the voltage and current are in phase, which is often the case in resistive loads:

    • P{ \text{ave}} = \frac{1}{2} I0 V_0

    • RMS (Root Mean Square) values align meaningfully to DC, allowing for simpler calculations:

    • P{ \text{ave}} = I{ \text{rms}} V_{ \text{rms}}

    • RMS Values:

    • I{ \text{rms}} = \frac{I0}{\sqrt{2}}

    • V{ \text{rms}} = \frac{V0}{\sqrt{2}}

Ohm's Law for AC Circuits

  • Applied to AC systems:

    • Average power in resistive circuits:

    • P{ \text{ave}} = V{ \text{rms}} I_{ \text{rms}}

    • P{ \text{ave}} = I{ \text{rms}}^2 R

    • P{ \text{ave}} = \frac{V{ \text{rms}}^2}{R}

    • Key factor: The resistance impacts power consumption similarly to DC circuits but is averaged over time to account for the varying nature of AC.

Key Calculations and Cases

  • Sample Problems:

    • What is the peak voltage for a 120 V AC power circuit?

    • Calculate peak power consumption for a 60 W AC light bulb at a given operating voltage.

    • Determine current needed to draw 100 MW from a source at 200 kV using the formula:

    • I = \frac{P}{V} where power (P) is given and voltage (V) is known.

    • Power dissipation in transmission lines with resistance (R) of 1 Ohm can be calculated as:

    • P = I^2 R

    • Percentage loss in transmission can be found using:

    • \frac{P{\text{loss}}}{P{\text{total}}} \times 100

Summary of Terms

  • Key Definitions:

    • AC current: Fluctuating current described mathematically as I = I_0 \times \text{sin}(2 \text{π}ft)

    • DC current: Constant flow of electricity in one direction.

    • Electric Power: Given by P = IV, representing the product of current and voltage over time.

    • Ohm's Law: For both AC and DC, I = \frac{V}{R}.

Glossary of Terms

  • Alternating Current (AC): Current that periodically changes direction, suitable for efficient long-distance power transmission.

  • Direct Current (DC): Current that flows in one direction only, typically used in batteries and electronics.

  • Resistivity: Intrinsic property of a material; ratio of resistance to its dimensions, affecting its ability to conduct current.

  • Resistance: Property that impedes current flow; given by R = \frac{V}{I}, dictating how much current will flow at a given voltage.

  • Root Mean Square (RMS): A statistical measure of the magnitude of a varying quantity, essential