Electric Fields, Ohm's Law, Magnetics

• Electric fields, Ohm's Law, power, magnetics, and transformers are fundamental concepts in electrical engineering
• These concepts govern the behavior of electric circuits and electromagnetic devices

Electric Field Concepts

• Electric fields are created by electric charges
• Electric field strength (E) is defined as the force per unit positive charge
• E = F/q, where F is the force on the charge and q is the magnitude of the charge
• The electric field is a vector quantity, having both magnitude and direction
• Electric fields are represented by electric field lines, which show the direction of the force on a positive charge
• Electric field lines originate from positive charges and terminate on negative charges
• Electric potential (V) is the electric potential energy per unit charge
• The electric potential difference between two points is the work done per unit charge to move a charge between those points
• V = W/q, where W is the work done and q is the magnitude of the charge
• The electric field is related to the electric potential by E = -∇V
• Capacitance (C) is the ability of a body to store an electrical charge
• It is defined as the ratio of the change in electric charge to the corresponding change in electric potential
• C = Q/V, where Q is the charge and V is the potential difference
• The energy stored in a capacitor is given by U = (1/2)CV^2

Ohm's Law Applications

• Ohm's Law states that the voltage across a resistor is directly proportional to the current flowing through it
• V = IR, where V is the voltage, I is the current, and R is the resistance
• Resistance (R) is the opposition to the flow of electric current
• It is measured in ohms (Ω)
• Resistors in series: The total resistance is the sum of the individual resistances (R_total = R1 + R2 + ...)
• Resistors in parallel: The reciprocal of the total resistance is the sum of the reciprocals of the individual resistances (1/R_total = 1/R1 + 1/R2 + ...)
• Ohm's Law can be used to analyze simple circuits containing resistors and voltage sources
• Kirchhoff's Current Law (KCL): The sum of the currents entering a node (junction) is equal to the sum of the currents leaving the node
• Kirchhoff's Voltage Law (KVL): The sum of the voltage drops around a closed loop is equal to zero
• Voltage dividers: Used to create a specific voltage level from a higher voltage source
• Current dividers: Used to divide current between parallel branches

Power Calculations

• Electric power is the rate at which electrical energy is transferred by an electric circuit
• Power (P) is calculated as P = VI, where V is the voltage and I is the current
• Using Ohm's Law, power can also be expressed as P = I^2R or P = V^2/R
• The unit of power is the watt (W)
• Energy (E) is the capacity to do work and it is calculated as E = Pt, where P is the power and t is the time
• The unit of energy is the joule (J) or kilowatt-hour (kWh)
• Resistors dissipate power in the form of heat
• The power dissipated by a resistor is given by P = I^2R
• Power sources (e.g., batteries, generators) supply power to the circuit
• The power supplied by a voltage source is given by P = VI
• Efficiency is the ratio of output power to input power
• Efficiency = (P_out / P_in) * 100%

Magnetic Field Theory

• Magnetic fields are created by moving electric charges
• The magnetic field strength (B) is measured in teslas (T)
• Magnetic fields are represented by magnetic field lines, which show the direction of the magnetic force on a moving positive charge
• Magnetic field lines form closed loops
• The magnetic force on a moving charge is given by the Lorentz force law: F = q(v x B), where q is the charge, v is the velocity, and B is the magnetic field
• The magnetic force is perpendicular to both the velocity and the magnetic field
• The magnetic force on a current-carrying wire is given by F = IL x B, where I is the current, L is the length of the wire, and B is the magnetic field
• Electromagnets are created by coiling a wire around a ferromagnetic core
• The strength of the electromagnet is proportional to the current and the number of turns in the coil
• Magnetic circuits are analogous to electric circuits
• Magnetomotive force (MMF) is analogous to voltage
• Reluctance is analogous to resistance
• Magnetic flux is analogous to current

Transformers

• Transformers are devices that transfer electrical energy from one circuit to another through electromagnetic induction
• A transformer consists of two or more coils of wire wound around a common core
• The primary coil is connected to the input voltage, and the secondary coil is connected to the load
• The turns ratio (N) is the ratio of the number of turns in the secondary coil to the number of turns in the primary coil (N = N_s / N_p)
• The voltage ratio is proportional to the turns ratio (V_s / V_p = N_s / N_p)
• The current ratio is inversely proportional to the turns ratio (I_s / I_p = N_p / N_s)
• Step-up transformers increase the voltage (N > 1)
• Step-down transformers decrease the voltage (N < 1)
• The power in the primary coil is approximately equal to the power in the secondary coil (assuming an ideal transformer)
• Transformers are used to change voltage levels, isolate circuits, and match impedances
• Ideal transformers offer lossless transofmrations
• Real transformers have losses due to hysteresis, eddy currents, and winding resistance