Current, Voltage, and Resistance Notes

17. 1 Current, Voltage, and Resistance

Electric Current

• Electric current is the movement of charge through a conductor due to a potential difference.

Current

• Stationary charges can attract or repel other charges, causing them to move.
• The direction and amount of movement depend on the potential difference between the charged particles.

Electrodynamics

• Electrodynamics is the study of the causes and effects of current electricity.

Electric Circuit

• An electric circuit is a collection of components connected in a way that allows electric current to do work.

Defining Current

• Electric current begins with a potential difference.
• Individual electrons do not move far from their original positions.
• An impulse of motion spreads, although the drift velocity is slow.

Defining Current

• Since current is the flow of charge, its unit, the ampere (A) is defined as 1 coulomb per second.
  1 A = \frac{1 C}{1 s}

Conventional Current

• Conventional current is the direction that positive charges move in a circuit.

Current Direction

• The direction of conventional current is the reverse of how electrons actually move.
• In solids, only electrons can move.
• The charges move in response to the electric field.

Direct Current (DC)

• Direct current is electric current that moves through a circuit in only one direction.

Alternating Current (AC)

• Alternating current is electric current that changes or alternates direction.

Potential Difference and Voltage

• VA – VB = –(VB – VA)
• Potential difference can be positive, negative, or zero.
• Polarity markings: positive (+) is used for the higher potential, negative (–) for the lower.

Electromotive Force (EMF)

• Electromotive force is the potential difference created by a self-contained device such as a battery; the amount of work the power source does to move charge through a circuit.

Potential Difference and Voltage

• A battery changes chemical energy to create electric potential.
• A photovoltaic cell changes light energy to create electric potential.
• An electromagnetic generator changes mechanical energy to create electric potential.
• A piezoelectric crystal converts mechanical strain to create electric potential.
• Potential difference is measured in volts (V), or joules of energy per coulomb of charge.
  1 V = \frac{1 J}{1 C} = 6.24 × 10^{18} e

Resistance

• The material through which electric charge travels impedes the current to some extent.
• As electrons move through a material, its temperature will rise.
• Both the material and its temperature affect how well it conducts electricity.

Resistivity (ρ)

• Resistivity is the tendency of a material to impede current.
• A superconductor has zero resistivity.

Resistor

• A resistor is a circuit component designed with a specific resistance to control current and voltage.

Resistance (R)

• Resistance is a characteristic of an electrical component that describes the degree to which the component impedes current.
• The geometry of a circuit component affects how well it conducts or resists the movement of electrons. R = ρ \frac{L}{A}
  • Where:
    • R is resistance
    • ρ is resistivity
    • L is length
    • A is area
• The unit of resistance is the ohm (Ω).
• A good conductor has a low resistance.

Example 17–1 Calculating Resistance

• A scientist has a 1. 5 m copper wire with a radius of 1.2 mm.
  • What is the resistance of the wire?
  • What would be the effect of using nickel instead of copper?
  • What would be the effect of doubling the length of the wire?
  • What would be the effect of doubling the radius?

Ohm’s Law

• The change of potential across any circuit component can be expressed as V = IR.
  • V = potential difference across the component
  • I = current through the component
  • R = resistance of the component
• The unit of resistance is the ohm (Ω).
  1 Ω = \frac{1 V}{1 A}
• While it is a good approximation, not all conductors follow Ohm’s law.

Example 17–2 Calculating Voltage

• An engineer measures 1. 54 A of current through a conducting wire with a resistance of 5.63 × 10^{–3} Ω. What is the potential difference across the wire?

Example 17–3 Calculating Current

• A scientist has a 333 Ω resistor with a potential difference of 12. 0 V across it. What is the current through the resistor?

Electrical Work and Power

• Electric components are intended to do work.
• Since work = potential difference × charge, W = Vq.
• Power is defined as the rate at which work is done: P = \frac{W}{Δt}.
• Since P = \frac{W}{Δt}, W = Vq, and I = \frac{q}{Δt}, we can derive P = VI.
• Using P = VI with Ohm’s Law, we can derive two more equations for electrical power (when there is a constant temperature):
  • P = I^2R
  • P = \frac{V^2}{R}
• Power is expressed in joules per second, or watts (W).
• 1 kW·h = 3,600,000 J
• The kilowatt-hour is used to measure the electrical energy used in homes.

Table 17-2 Some Basic Electrical Dimensions

Example 17–4 Calculating Power Consumed

• A typical toaster operates on a 120. 0 V system. If the internal resistance is 12.46 Ω at full temperature,
  • how much power does it consume
    P = \frac{V^2}{R} = \frac{(120.0 V)^2}{12.46 Ω} = 1155.6 W
  • how much energy (in kW·h and joules) will it use to make toast if it runs for 95. 0 s?
    E = Pt → E = (1155.6 W)(95.0 s)
    E = (1155.6 \frac{J}{s})(95.0 s) = 1.10 × 10^5 J
    E = (1155.6 W)(95.0 s) = 0.0305 kW·h

Talking Tech Trash

• What happens to old electronic devices? Are they a hazard to the environment or to people?

Example 17–5 Calculating Current and Energy

• A plasma TV has a power rating of 345 W.
  • How much current passes through the TV when the potential difference is 120. 0 V?
  • How much energy (in kW·h and joules) would it use if left on all day?
  • How much does it cost to leave it on all day if electricity costs $0. 12 per kW·h?

Calculating Current and Energy

• By knowing the current going through an electrical device and the voltage drop in the device, we can determine the electrical power consumed by the device.
• We can determine the energy by factoring in the amount of time the device is used.