Resistors in Series

Study Notes

Resistors in Series

When multiple resistors are connected in series, the total voltage (Vtotal) is shared among them.
The voltage across each resistor is proportional to its resistance.
If the resistors are identical, the voltage across each resistor is equal.
The total voltage is equal to the sum of the voltages across each resistor: Vtotal = V1 + V2 + ...
The total current is the same for all resistors in series: I = Vtotal / Rtotal
The total resistance is the sum of the individual resistances: Rtotal = R1 + R2 + ...

Resistors in Parallel

When multiple resistors are connected in parallel, the voltage across each resistor is the same.
The current through each resistor is proportional to its resistance.
The total current is the sum of the currents through each resistor: Itotal = I1 + I2 + ...
The reciprocal of the total resistance is the sum of the reciprocals of the individual resistances: 1/Rtotal = 1/R1 + 1/R2 + ...

Potential Dividers

A potential divider is a series circuit with two resistors.
The voltage across each resistor is proportional to its resistance.
The ratio of the resistances is equal to the ratio of the voltages: R1/R2 = V1/V2
The voltage across a resistor can be found using the total voltage and the ratio of resistances: V1 = Vtotal * (R1 / (R1 + R2))
Potential dividers can be used to control the voltage supplied to a device or circuit.

Thermistors and LDRs

A thermistor is a type of resistor whose resistance changes with temperature.
A light-dependent resistor (LDR) is a type of resistor whose resistance changes with light.
Potential dividers can be used to control devices or circuits based on temperature or light levels.
Examples of applications include turning a heater on when it gets too cold, turning a fan on when it gets too hot, or turning a street light on when it gets too dark.

Resistors in Series

Total voltage is shared among resistors, with each resistor having a voltage proportional to its resistance.
Identical resistors in series have equal voltage across each.
Total voltage is the sum of individual voltages: Vtotal = V1 + V2 +...
Total current is the same for all resistors: I = Vtotal / Rtotal.
Total resistance is the sum of individual resistances: Rtotal = R1 + R2 +...

Resistors in Parallel

Each resistor has the same voltage across it.
Current through each resistor is proportional to its resistance.
Total current is the sum of individual currents: Itotal = I1 + I2 +...
Reciprocal of total resistance is the sum of reciprocals of individual resistances: 1/Rtotal = 1/R1 + 1/R2 +...

Potential Dividers

A potential divider is a series circuit with two resistors.
Voltage across each resistor is proportional to its resistance.
Ratio of resistances is equal to the ratio of voltages: R1/R2 = V1/V2.
Voltage across a resistor can be found using the total voltage and the ratio of resistances: V1 = Vtotal * (R1 / (R1 + R2)).
Potential dividers can be used to control the voltage supplied to a device or circuit.

Thermistors and LDRs

Thermistors are resistors whose resistance changes with temperature.
LDRs are resistors whose resistance changes with light.
Potential dividers can be used to control devices or circuits based on temperature or light levels.
Applications include temperature-based control (e.g., heaters, fans) and light-based control (e.g., street lights).

Description

Learn how to calculate total voltage, current, and resistance when multiple resistors are connected in series. Understand how voltage is shared among resistors and how to apply formulas to solve problems.