EE Study Notes

Ohm’s Law

V = IR where V is Voltage, I is current and R is resistance Current and Resistance are directly proportional to voltage. i.e. if current/resistance increase,

voltage also increases Current is inversely proportional to resistance. i.e. If current increase, resistance decrease and

vice versa

Resistors in Series

Total voltage = sum of voltage across all resistors in series. Vt = V1 +V2 + V3

Total resistance = sum of all resistors in circuit. i.e. Rt = R1 + R2 + R3 + …..

The current through all the resistors is the same.

Resistors in Parallel

Voltage across all resistors in a parallel circuit is the same. V = V1 = V2 = V3

Total current = sum of all current travelling through each resistor Total resistance:

Power, Energy & Efficiency

Unit of Charge: Coulomb (Q) Unit of Energy : Joules (J) or kWh (kilowatt-hours) Unit of Power : Watts or J/s (W)

Energy = I2Rt joules = Power x Time

Power = Voltage x Current P=IV The total power for both series and parallel circuits, is equal to the sum of the powers in each

resistor :

PT = P1 + P2 + P3 + … … + Pn

Efficiency:

Cells Types of cells

o Wet Leclanche Cello Dry Leclanche Cello Mercury Cello Carbon-Zinc Dry Cello Alkaline-Manganese Cell

Internal Resistance

V = E – IrV = IR

where V = terminal voltage of cell E = open circuit voltage of cell r = internal resistance of cell R = load resistance I = load current

The emf (E) of a cell is the total voltage generated by the cell is measured with the cell open-circuit (also called open circuit voltage of cell).

The terminal voltage, or potential difference (p.d.) of a cell, is the voltage across the cell terminals when the cell is supplying current to a load

Capacitors

A capacitor is a device which stores energy in the form of electric charge. Symbol : C, Unit: Farad (F) Capacitance = Charge / Voltage

The larger the capacitance, the larger will be the charge stored. Capacitance (C) is directly proportional to the dielectric permittivity ().

Capacitors in Parallel & Series

In series: 1CT

= 1C1

+ 1C2

+ 1C3

In Parallel: CT = C1 + C2 + C3 + ... ... + Cn

AC Circuits

Period - The time required for a given sine wave to complete one full cycle.o symbol - To unit - second (s)

Period Measurement - From one zero crossing to the corresponding zero crossing in the next cycle

Frequency - The number of cycles a sine wave can complete in 1 second.

o symbol : fo unit - Hertz (Hz)

Frequency vs Period

If an ac voltage is applied to a circuit, an ac current flows. The voltage and current will have the same frequency.

Ways to express and measure the value of a sine wave :o instantaneous value.o peak value.o peak-to-peak value.o root-mean-square value.o average value.

Peak Value - The voltage or current value of a waveform at its maximum positive or negative points.

o Vp or Vmax

o Ip or Imax

Peak-to-Peak: The voltage or current value of a waveform measured from its minimum to its maximum points.

o Vpp or Ipp

o Vpp = 2 x Vmax or Vmax = 0.5 x Vpp

Root Mean Square Valueo Vrms = 0.707 x Vmax

Average Valueo Vavg = 0.637 x Vmax

Phasor Diagram

There are three ways to describe the phase angle in a phasor diagram:

1. Same phase or in phase

2. Leading

3. Lagging

Characteristics of A.C. Pure Resistive Circuit o Voltage and current are equally opposed by the circuit.o The current(I) flows through the resistor is in-phase with the applied voltage(V). o The phase angle between the applied voltage and current is 0°

Characteristics of A.C. Pure Inductive Circuit o There is opposition to current flow.o Current flows through the pure inductor lags the applied voltage by 90°. o The phase angle between the applied voltage and current is 90°. ( = 90° )

XL : inductive reactance(), f: Frequency(Hz), L: Inductance(H)

V I = ---- R

XL = 2 f L

Characteristics of A.C. Pure Capacitive Circuit o Current flows through the pure capacitor leads the applied voltage by 90°. o The phase angle between the applied voltage and current is 90°. ( = 90° )

Xc: Capacitive reactance(), f: Frequency(Hz), C: Capacitance(F)

Impedence

Characteristics of A.C. RL Series Circuit o Current is in phase with VR.o Current lags VL by 90o.o Current lags VS by where is the phase angle or phase difference.

Impedence: The opposition to the current flow is called the impedance. o Symbol : Zo Unit : Ohms ( )

Formulae:o Vs = IZ where Vs = supply voltage, I = current, and Z = impedence

o where Z = impedence, R = Resistance, and XL = inductive reactance

Characteristics of A.C. RC Series Circuit o Current is in phase with VR.o Current leads VC by 90o.o Current leads VS by where is the phase angle or phase difference.

Formulae:o Vs = IZ where Vs = supply voltage, I = current, and Z = impedence

o where Z = impedence, R = Resistance, and Xc = capacitive reactance

1Xc = --------- 2 f C