Circuits
Physics: AQA A Level, topic 5.1.8
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, , is the sum of the reciprocal resistances in the network.
- It can be written for a network of n resistors as:
Resistors in series
- The total resistance is the sum of each individual resistor.
- The equation for the total resistance is:
- 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.
Test yourself on Circuits
How does the total resistance of a parallel circuit relate to the individual resistors?
What is the equation for the total resistance in a parallel circuit?
Which of these statements are true about resistors?
How is conservation of charge represented in a parallel circuit?
What is Kirchoff's current law?