Question

Design circuits that demonstrate all of the principles listed below. Set up the circuits and take measurements to show that the principle in question is indeed correct.
Principles of Series Circuits:
The voltages across each circuit element add to that of the battery.
The current through each circuit element is the same.
Higher resistances have higher voltage across them.
Resistors added in series to any circuit increase the resistance to current in the circuit.

Principles of Parallel Circuits:
Voltages across each circuit element are the same.
The current through each parallel circuit element adds to that going through the battery.
The higher resistance in a parallel circuit has less current.
Resistors added in parallel to any circuit reduce the resistance to current in the circuit.

General Principles:
A branch in a circuit that contains a short has no voltage across it.
A branch in a circuit that is open has all the voltage across it.
A battery is a constant voltage source.
A battery is not a constant current source.
Ammeters have very little internal resistance.
Voltmeters have very large internal resistance.

Answer 1

Explanation:

For series

$\Delta V=V_{1}+V_{2}+\ldots+V_{n}=I R_{1}+I R_{2}+\ldots+I R_{n}(\text {voltages add to the batter } y)$

$\(I=I_{1}=I_{2}=I_{n}\) (current is the same)$

$V=I R(\text {voltage is directly proportional to } R)$

$R_{e q}=R_{1}+R_{2}+\ldots+R_{n} \quad \text { (resistance increase) }$

For parallel

$\Delta V=\Delta V_{1}=\Delta V_{2}=\Delta V_{n} \quad(\text { same voltage })$

$I=I_{1}+I_{2}+\ldots+I_{n}(\text {current adds})$

$\(I=\frac{\Delta V}{R_{e q}} \quad(R \text { inversal } y \text { proportional to } I)\)$

$\frac{1}{R_{e q}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\ldots+\frac{1}{R_{n}}$