5.1.8

# Circuits

Test yourself

## Resistors in Circuits

The total resistance of resistors in parallel is always less than the smallest resistor in the parallel network.

### Resistors in parallel

• The reciprocal total resistance, $\frac{1}{R_{total}}$, is the sum of the reciprocal resistances in the network.
• It can be written for a network of n resistors as:
• $\frac{1}{R_{TOTAL}}= \frac{1}{R_1}+\frac{1}{R_2}+⋯+\frac{1}{R_n}$

### Resistors in series

• The total resistance is the sum of each individual resistor.
• The equation for the total resistance is:
• ${R_{total}}={R_1}+{R_2}+...+{R_n}$
• Where n is the number of resistors.

## Current in Parallel Circuits

Current in parallel circuits splits up like a river's current.

### Kirchhoff's first law

• The total current arriving at a junction is equal to the total current leaving a junction.
• The current labelled is conventional current (positive to negative).
• For electrical parallel circuits, this results in the familiar "current splits up" rule.
• This is a demonstration of the conservation of charge. Charge cannot be created or destroyed.

## Voltage in Parallel Circuits

The sum of voltage drops in a closed loop must be equal to zero.

### Kirchhoff's second law

• The sum of voltage drops in a closed loop must be equal to zero.

### Kirchhoff's second law 2

• This also applies to having identical cells in parallel.
• The voltage drop across a reversed cell is negative because a positive charge does work against the positive end of the cell.

### Kirchhoff's second law 3

• This is a demonstration of the conservation of energy.
• If the sum of voltage drops was not zero, there would be either the destruction or creation of energy - which is impossible.

## Unlock your full potential with GoStudent tutoring

• Affordable 1:1 tutoring from the comfort of your home

• Tutors are matched to your specific learning needs

• 30+ school subjects covered

Book a free trial lesson