Total Resistance

Total Resistance in Circuits

General Concepts

• Resistance is a measure of how much a component reduces the electric current flow through it. It is defined by Ohm’s Law, R = V/I where R is resistance, V is potential difference (voltage) and I is current.
• The resistors in a given circuit, whether they be physical components or intrinsic properties of elements of the circuit, all contribute to the total resistance of the circuit.

In Series Circuits

• In series circuits, total resistance (R_total) is simply the sum of all individual resistances: R_total = R1 + R2 + R3 + … etc.
• Total resistance will increase as more resistors are added in series, leading to a decrease in total current flowing through the circuit.

In Parallel Circuits

• Within parallel circuits, the calculation for total resistance (R_total) is less straightforward. Use the formula: 1/R_total = 1/R1 + 1/R2 + 1/R3 + … etc.
• Adding more resistors in parallel decreases the total resistance which leads to an increase in total current flowing through the circuit.

Ohmic and Non-Ohmic Components

• Components with a constant resistance that do not change with voltage or current are referred to as ohmic.
• Conversely, components which have resistance that changes with voltage or current are referred to as non-ohmic. Examples can include filament lamps or diodes.

Resistance and Temperature

• For many materials, particularly metals, resistance tends to increase as the temperature increases. This is due to increase in energy causing ions in the metal to vibrate more and block the flow of electrons causing an increase in resistance.
• Components made of materials like silicon or germanium, however, exhibit the opposite property: resistance decreases as temperature increases.