EE Study NotesOhm’s Law V = IR where V is Voltage, I is current and R is resistance Current and Resistance aredirectly 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 versaResistors 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 totalpower for both seriesand 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 Cell o Dry Leclanche Cell o Mercury Cell o Carbon-Zinc Dry Cell o Alkaline-Manganese CellInternal ResistanceV = E – IrV = IRwhere 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 loadCapacitors 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: 1 1 1 1 CT C1 C2 C3
In Parallel: CT = C1 + C2 + C3 + ... ...+ CnAC Circuits Period - The time required for a given sine wave to complete one full cycle. o symbol - T o 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 : f o 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 Vpor 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 Value o Vrms= 0.707 x Vmax Average Value o Vavg= 0.637 x VmaxPhasor 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° V I = ---- R 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 = 2 f L XL: inductive reactance( ), f: Frequency(Hz), L: Inductance(H)
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° ) 1 Xc = --------- 2 fC 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 : Z o 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