Resistors in Parallel: Self-assessment

Harmonics and RMS Values

• An even multiple of the fundamental is an even harmonic.
• The effective value of a harmonic quantity is obtained by:
• First, obtaining the square of the RMS value of each term.
• Adding the obtained squared RMS values.
• Taking the square root of the sum.

Phasors

• Phasors are used to represent sinusoidal quantities to avoid drawing sine waves.
• A phasor is a straight line whose length is proportional to the RMS voltage or current it represents.
• Phasors bear an arrow to show the phase angle or phase displacement between voltages and currents.

Phasors in Phase and Out of Phase

• Two phasors are said to be in phase when they point in the same direction.
• The phase angle between them is then zero.
• Two phasors are said to be out of phase when they point in different directions.
• The phase angle between them is the angle through which one of them has to be rotated to make it point in the same direction as the other.

Resistors in Parallel

• The total resistance RT is given by: 1/RT = 1/R1 + 1/R2.
• Effective circuit resistance is found by identifying and putting together series and/or parallel resistors.

Effective Resistance of a Circuit

• Examples of finding the total resistance of a circuit are provided, including circuits with multiple resistors in parallel and series.

Current Division Rule

• The current division rule is applied to share current between parallel branches.
• The rule is used to find the current in each branch.

Phasor Diagrams

• Phasor diagrams are used to show the magnitude and phase relations among the various quantities within a network.
• Phasor diagrams are often helpful in the analysis of the network.

Addition and Subtraction of Sinusoidal Quantities

• The sum of sinusoidal quantities is obtained by taking the vector sum of their phasors.
• The difference of sinusoidal quantities is obtained by first reversing the subtracted quantity and adding it as a vector to the other phasors.
• A sinusoidal quantity is reversed by adding 180° to its angle.
• Only sinusoidal quantities of the same frequency can be added or subtracted.

Impedance (Z)

• The impedance of a circuit is a measure of the total opposition to current flow.
• Examples of finding the impedance of a circuit are provided, including circuits with resistors, capacitors, and inductors.

Power in AC Circuits

• There are three kinds of power in ac circuits:
• Apparent Power (S) measured in Volt-amperes (VA).
• Active Power (P) measured in Watts (W).
• Reactive Power (Q) measured in Volt-amperes reactive (VAR).

Root Mean Square (RMS) Value

• The RMS value is the square root of the mean of the squared values.
• The RMS value is used to calculate the effective value of a sinusoidal quantity.
• The RMS value is used to calculate the power in an AC circuit.

Sinusoidal Voltages and Currents

• Voltages and currents of commercial ac generators have the following expressions:
• v = Vm sin ωt or v = Vm sin 2πft.
• i = Im sin ωt or i = Im sin 2πft.
• The peak voltage Vm and peak current Im are the maximum values of the voltage and current, respectively.

Test your understanding of resistors in parallel by identifying which resistors are connected in parallel in a circuit. Calculate the total resistance when resistors are in parallel. Determine the effective resistance of a circuit by combining series and parallel resistors.