Multiple Path Circuits and Factors Affecting Resistance

This set of vocabulary flashcards covers electrical circuit principles including Ohmic calculations, factors affecting the resistance of conductors (length, CSA, material, temperature), and laws governing parallel circuits.

Direct Proportionality of Length

The relationship where the resistance of a conductor is directly proportional to its length; if the length is doubled, the resistance also doubles ($\frac{R_1}{R_2} = \frac{l_1}{l_2}$).

Inverse Proportionality of Cross-Sectional Area (CSA)

The relationship where the resistance of a conductor is inversely proportional to its cross-sectional area; if the CSA increases, the resistance decreases ($\frac{R_1}{R_2} = \frac{A_2}{A_1}$).

Cross-Sectional Area Formula

An equation related to conductor diameter used to find the area: $A = \frac{\pi d^2}{4}$, where $A$ is area and $d$ is diameter.

Resistivity

A material property, pronounced "row" ($\rho$), that describes how strongly a material opposes current flow; higher resistivity results in higher resistance.

Resistance Equation (Material, Length, CSA)

The mathematical formula expressed as $R = \frac{\rho l}{A}$, where $R$ is resistance in ohms, $\rho$ is resistivity in ohm-metres, $l$ is length in metres, and $A$ is CSA in $m^2$.

Positive Temperature Coefficient (PTC)

A property of most metallic conductors where an increase in temperature results in an increase in resistance.

Negative Temperature Coefficient (NTC)

A property where an increase in temperature results in a decrease in resistance, often found in components for appliances like fridges.

Final Resistance Formula (Temperature)

The formula $R_2 = R_1[1 + \alpha(t_2 - t_1)]$ used to calculate resistance changes based on temperature, where $\alpha$ is the temperature coefficient of resistance.

Power Loss (Heat)

The dissipation of energy in a conductor due to resistance, calculated using the formula $P = I^2 R$.

Voltage Drop

The reduction in voltage across circuit conductors caused by resistance, calculated as $V = IR$; the maximum allowable drop permitted by AS/NZS 3000 in a $230\,V$ installation is $5\%$.

Parallel Voltage Rule

The law stating that in a parallel circuit, the same voltage appears across every component: $V_T = V_1 = V_2 = V_3…$

Kirchhoff's Current Law

The principle stating that the sum of the currents entering a junction equals the sum of the currents leaving that junction ($I_T = I_1 + I_2 + I_3…$).

Total Resistance in Parallel (General Equation)

The reciprocal relationship for finding equivalent resistance: $\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}…$

Product over Sum Method

An alternate method for calculating the total resistance of exactly two resistors in parallel: $R_T = \frac{R_1 \times R_2}{R_1 + R_2}$.

Resistance Divided by Number of Components (R/n)

A simplified method to determine equivalent resistance ($R_T = \frac{R}{n}$) when all resistors in a parallel circuit have the same ohmic value.

Total Power Dissipated in Parallel

The value equal to the sum of the individual power values dissipated by each component: $P_T = P_1 + P_2 + P_3…$